We've been walking through the districts of Lima for three hours, snaking our way through Miraflores and up towards San Isidro. It is said that these are the streets upon which Lima's elite congregate to sample the finest cuisine South America has to offer, and where tourists flock to soak up a little metropolitan culture before setting off for the bucolic pleasures of the Gringo Trail. Peru's gastronomic revolution unfolded here, with many crediting the husband-and-wife duo behind San Isidro hotspot Astrid y Gaston for the country's blossoming culinary reputation. All of the guides tell us that these two districts in Lima are the places to be; there are museums, art galleries, restaurants, bars, cafes, everything you could want.

So why the fuck can't we find anything to see or do?

It's Day 1 of our month in Peru, and I am jet-lagged and confused. They say that culture shock takes months to develop, however I seem to have already bypassed the honeymoon phase (which is ironic seeing as I am here with my new husband on our honeymoon) and am thoroughly rooted in the, well, shocked phase. The first jolt came when we entered the city centre the night before in an airport-approved taxi, which nevertheless was the single most terrifying car journey of my life. Official guidance states that you should only ever use officially approved companies for fear of corrupt drivers who participate in organised robberies. However, taking the safer option doesn't immunise you against the MarioKart style road acrobatics that are so favoured by Peruvian taxi drivers, who are prone to using their horns more liberally than their brakes. Within minutes I've gone from staring at palm trees with dreamy-eyed joy, to clutching the edge of my seat and desperately hoping for the best.

The next travel tips that must be heeded involve the plumbing. Although Peru has plugged sufficient funds into the development of the sanitisation system in Lima over the past decades, travellers should still be warned that it is inadvisable to drink the tap water, and flushing toilet paper is a big no-no. This is my first time in a country where this is the case and whilst my sense of adventure is willing to accommodate this for the sake of an incredible trip, perhaps sharing a shit bin with my husband for a month isn't quite the right way to kick-off married life.

But despite all this, the thing that's really getting to me is the fact that we just cannot seem to be able to locate any kind of "centre" at all. I'm looking for plazas and pavement cafes, pockets of the city where one can just "be" entirely effortlessly. In my mind's eye, Lima should be all uninterrupted blue skies, elaborate villas and cascading florals with a peppering of museums and galleries on every block. So far it hasn't materialised - instead we have walked past uninspiring concrete blocks and haphazard houses in a haze of choking smog from the retro vehicles on the road. In addition, Huaca Pucllana, the great ancient adobe we had planned to explore for the morning, is closed for the day. We are wandering aimlessly down almost-deserted roads, with no plan and no internet access. But I am determined to find this elusive dream of mine. Despite the exhaustion and the confusion, I haven't given up on Lima quite yet.

Our first taste of beauty arrives as we wander down a nondescript road, just one block away from the Via Expresa motorway that cuts up the heart of the city. As we pass beneath some frothing pink blooms, a quivering shape above our heads catches our eye. It's a hummingbird and I feel a burst of excitement in my chest as I try to catch the little creature with my camera (I fail). Continuing along down the road, I begin to peer more closely at the trees and flora surrounding us, hoping to catch another glimpse of one. Eventually we arrive in the Bosque del Olivar, a 57 acre park containing 1,675 olive trees whose roots stretch back to just three small trees that arrived on Peruvian soil in 1560. From our bench, we watch the park wardens and the dog walkers meandering between the gnarled, ancient trunks, whose branches stretch outwards in petrified longing. There's an overwhelming sense of peace here, with countless little birds flitting between trees and hopping down the paths; amongst them are long-tailed mockingbirds, West Peruvian doves and shrub blackbirds, whose sleek jet coats shine indigo in the light. Every now and then, the intricate song of some unseen feathered creature weaves through the air. Later as we leave the park, we come across a charm of saffron finches nestled between the roots of an olive tree, tiny golden birds who tremble and glide through the air.

From this moment onwards, our strategy for navigating Lima involves designing routes that take us through as many parks as possible. Much of this sprawling metropolis is made up of densely packed buildings, with a startlingly sudden discord between the rich and the poor areas. Walking back to Miraflores from the historic centre on our second day, we find ourselves crossing from dirty-walled, cramped housing with brittle-looking tinted windows, to palatial villas and sleek apartment buildings within a matter of minutes. Something that all of these residential areas have in common, however, is that incessant haze of fuel that curls up your nostrils and down into your throat. I have never been anywhere as suffocatingly polluted as Lima, and the parks that are threaded through the city's blocks offer a welcome escape. It is in these open green spaces, where the city's workers come to rest and eat their fabulous-looking lunches from tupperware boxes, that we can breathe freely again as we watch curiously marked squirrels spiralling around tree trunks.

 On our first day, our planned lunch spot  is closed (we'd hoped to visit El Mercado in Miraflores, which received glowing reviews here), so in a fog of exhaustion, we bundle ourselves into the nearest cafe, El Pan de la Chola, which just so happens to be the most hipster place in Miraflores. Heeding the advice about eating raw vegetables, we ignore the temptations of fresh avocado and tomato and order simple cheese sandwiches - which turn out to be the most incredible oozing slabs of cheese, barely contained between two slices of expertly-baked focaccia. They are huge and delicious, and yet I still feel that I need a little something more to help perk me up. Not normally being a fan of hot chocolate, I nevertheless decide that I need some liquid sugar and end up happily discovering that Peruvian chocolate caliente bears no resemblance to the weakly flavoured hot milk I have tasted in the UK. It is thick and spiced and possibly honeyed - but best of all it actually tastes like chocolate. This single cup changes my outlook forever, and sees me obsessively tracking down the best hot chocolate in each of our Peruvian destinations for the remainder of the month (Lima's best picks for me are El Pan de la Chola and Miss Cupcakes, both in Miraflores).

The gastronomic delights continue on our second day when we visit Astrid y Gaston, the famed and aforementioned restaurant. Having been gifted a meal as a wedding present, we are treated to a cacophony of flavours and colours, tasting our way through three centuries of ceviche (the original version of this famous dish dating from the 19th century involves marinading chunks of the freshest fish in a simple, zesty orange juice), perfectly cooked sea bass with a foamy lima bean accompaniment, and the most surprising dessert - a chocolate globe as large as a football which is cracked open with table spoons to unveil an explosion of mousse and fruit and cream and more chocolate hiding inside. As hard as we try, it's impossible to get even close to finishing it - and we understand why when we spot another table ordering one for four people rather than two.

After forcing down some delectable petit fours and a few cups of hierba luisa tea (a plant from the verbena family which makes a sweetly lemon flavoured brew and becomes a firm favourite of mine throughout the trip), the only thing left to do is to continue walking - the main pastime we fill our days with in Lima. The air is cool but pleasant although this is mainly due to the fact that for the entire duration of our five-day stay in the city (which is split into two days at the beginning of the month, and three days at the end), Lima is enveloped in its iconic coastal fog. It is surprising just how much moisture can be retained in the air of the world's second driest capital, but there you go. These mists that roll in off the ocean preclude our ability to admire the views of coastline stretching far off into the distance, but as we walk through the parks that line the crumbling, black clifftops, the sight of the Pacific disappearing into a silver haze long before the horizon is due constitutes a unique beauty in itself. And whilst the Pan-American Highway roars along with the waves down at the foot of these cliffs, these coastal walks on the edge of the continent provide the perfect antidote to a morning spent buried in the depths of the city.

One such excursion to the heart of Lima is our visit to the Basilica y Convento di San Francisco. Nestled in the historic centre, the monastery is only accessible by guided tour, on which strictly no photos are allowed. Here we are introduced to artworks in the style of the Cusco school (whose depictions of Catholic saints painted to resemble the Andean people are bestowed with a fairytale-like quality) and allowed to step through a beautiful wooden library containing thousands of antique volumes spanning half a millennium. We admire the Moorish ceiling carvings, walk down passageways painted in ivory and terracotta, and hear of the earthquake that brought so much of this monastery to its knees. Finally, we descend into the catacombs, a series of tunnels with an unnerving one-way system and rows of bones and skulls organised neatly into patterns. As we descend, the air that rushes to greet us is unexpectedly warm instead of the usual subterranean cool; a remnant of the Peruvian summer trapped beneath the monastery's stones.

And then finally, I find the version of Lima I'd been looking for. When we return at the end of the month, we choose Villa Barranco as our hotel, an elegant villa in the district of - you guessed it - Barranco. Whilst there are still no blue skies, Barranco is bursting with the ornate summer homes of the 19th and 20th century Limeños, and there are bars and cafes and museums everywhere. Once upon a time, this district used to be the fashionable seaside resort of Lima's high society; nowadays these glorious palaces house restaurants and artisan's workshops and art galleries, and so the doors to what were once the most exclusive addresses are now thrown open for anyone to enjoy.

We walk a short distance, past the crumbling Iglesia de Ermita, over the Puente de los Suspiros (make sure to hold your breath and make a wish as you cross for the first time) and along to the Parque Municipal, where the locals are sitting and chatting on benches whilst their children play football in front of the pink birthday cake of a library. Further down the avenue, we find the MATE Mario Testino Museum (which I have some reservations about visiting given the recent allegations) and the Pedro de Osma Museum, which houses a lavish collection of those beautiful Cusco school paintings within one of the most opulent mansions around. At the other end of the district is the Museo de Arte Contemporáneo (MAC), which (much in the style of the hot chocolate revelation) turns out to be the first modern art gallery that I can visit from start-to-finish without dissolving into a fit of sarcastic irritation. I particularly love the exhibition of Georges Rousse's works, a photographer who visits abandoned buildings and fills them with sculptures and optical illusions.

Our hotel helps to continue Barranco's air of vintage glamour in the way that it faultlessly blends the villa's heritage with more modern design features. Antique furniture sits next to contemporary artwork against a backdrop of high ceilings and parquet floors. Comfort is clearly key here, with vast beds buried under countless pillows and cushions. Our Junior Suite room has windows on two sides and a small balcony with a glimpse of a sea view. After a night away in Paracas, we move to a Superior Suite which is less airy and light but has a much larger balcony with comfortable deckchairs and a huge bathroom in whose sizeable bathtub I take a nice deep soak after a busy day. Breakfast has everything we could want, with fresh fruit, cheeses, hams, breads, cereals, jams and cake, with the option of freshly cooked eggs or pancakes. On one afternoon, I order a causa limeña from the room service menu to tide me over to dinner. Layers of salted mashed potato, creamy avocado, tomato and tuna with a scattering of olives - it is absolutely delicious. I notice how they have also thought to cut the skins off the tomatoes for the weary traveller (which, by the end of the month, I am). This is typical of the service we receive at the villa; care and thoughtfulness towards all guests is evident in every interaction. Every time we ring the doorbell to be let in, we are greeted at the gate as if this is our home, a sentiment that echoes in our ability to pad downstairs in our pyjamas at night and help ourselves to tea in the lounge.
 We end up finishing our time in Lima as we began; wandering aimlessly around the streets and eating. This time, Barranco offers us a never-ending gallery of street art to peruse and we have fun trying to hunt out as many murals as we can. We stop at La Panetteria Barranco for pastel de acelga (a kind of chard tart that interestingly originated n Italy), and eat neapolitan-style pizza and cheese toasties at Pan Sal Aire, a small restaurant full of groups of millenials happily sharing intriguing looking dishes. We finish up wth the densest salted-chocolate tart accompanied by a neat row of caramelised almonds.

But our last dinner in Peru is spent at Isolina, one of Barranco's best loved restaurants - and certainly not a place to take vegetarians. We arrive early in order to grab one of the walk-in tables on the first floor. Having been lauded as one of South America's best restaurants, the decor is much simpler than expected with bare wooden tables and a string of world flags hanging over our heads. As a pescatarian, the options are limited so I choose the only two fish dishes (ceviche followed by the famous fish sandwich). As these are both on the starter menu, I supplement them with side orders of chips and beans. We have read online that Isolina is big on portions, with the idea being that dishes are shared around the table. Our waiter further emphasises this point when we come to order and so we opt for individual portions so that Michele can enjoy some of the meat dishes they are famed for.

When everything arrives, the table can barely contain the sheer quantity of food we have ordered. And these are only the individual portions. A nearby table of Northern Americans can be heard gasping above the din of conversation when their meal arrives, such are the portion sizes at Isolina. Luckily we have both quality and quantity and everything is delicious, to the extent that I manage to both finish my ceviche and fish sandwich, and make a serious dent in the fries and beans (as well as the rice accompaniment to Michele's meat stew). It's a marvellous end to the trip, as we chat and eat and chat and eat until we can barely bear to spear our forks into a single morsel more. There is no way that we can face going back to the hotel like this, so we try to walk our gargantuan meal off with an amble down the Bajada de Baños, the passageway that once led Lima's holiday makers down to the old baths on the seafront. Those baths are no more, and the bajada has certainly lost the refined air it must have once held, but I still want to make this last minute pilgrimage to the sea. We cross a bridge that leads us over the highway and to the shore, dodging boys skating along the paths and groups of people smoking in the shadows. And then there's the ocean, right beneath my toes, crashing into the pebbles and then dragging them backwards, the rush and boom of the waves giving way to the strangely haunting sound of hundreds of stones cracking against each other as they tumble backwards with the tide. By the time we leave Lima, I feel that I have found what I was looking for.