This article appears in SUITCASE Volume 21: The Islands Issue

Leonard Leonard Cohen was living on the Greek island of Hydra in the 1960s with his girlfriend Marianne Ihlen (of So Long, Marianne fame) when he stared out the window of his white house in the hills and saw a newly installed telephone wire. "Civilisation had caught up with me," he said of this moment of realisation. "I wasn't going to be able to escape after all. I wasn't going to be able to live this 11th-century life that I thought I had found for myself." It was, on the upside, also the moment that would inspire his seminal masterpiece Bird On The Wire.

As I step off the boat from Athens and on to the cobbled harbour of Hydra, I understand why Leonard (can I call him Leonard? Forgive me - after making a pilgrimage to his beloved isle I feel as though we're on first-name terms) was anxious that this exquisite Saronic island should not be dragged by its feet into abrasive modernity. It is a unique time capsule of a less complicated world. There are no cars - only mules and donkeys for transport. There are posters and notes about local concerts and films at the small open-air cinema pinned to town noticeboards. Sharp, moneyed, modern architecture has somehow managed not to encroach on the predominantly white and terracotta vista. Even with its phone wires, you can't shake the soothing feeling that you have the same view over the Aegean Sea that Leonard and Marianne had in the Sixties, if not the exact 11th-century one that he longed for.

I am greeted at the chic Hotel Orlo , a short walk from the harbour, with a cool glass of lemonade. The hotel is elegant and rustic, with clean blue-and-white interiors adorned with antiques that nod to the island's heritage. It was built in 1796 by Count Orlo of Russia on the remains of a convent. I stay in a beautiful double room in a monasterial arcade, but I'm assured by the woman who shows me to it that they've caught up with 21st-century life enough to provide strong wifi. (I've noticed on my travels, rather depressingly, that the first thing a hotel receptionist often does is assure me that there is wifi, whether I've asked or not. I really must look like a frazzled Londoner.)

Right next to the hotel is the Rafalias Pharmacy, established in 1890 by the grandfather of the current owner and pharmacist. The charming shop, shrouded in apothecary cabinets and ancestral photos, has retained all its original features, as well as its original alchemies. The current owner preserved his late mother's notebook, which contained recipes for creams, perfumes and oil blends based on Greek pharmacology of the Twenties, and the shop still manufactures these beautifully packaged products. I pick up a pale-pink pot of olive-oil face cream, promising anti-ageing and skin-firming. I also buy a bottle of the oral Kyriaki perfume, which is the Greek word for Sunday. "Named after my maaatha," the current owner tells me, like a good Greek boy.

There are plenty of other treasure troves of tradition to be found in Hydra. Just off the harbour front there is a tablecloth shop selling crisp white linen, embroidered napkins, table runners, lace and placemats. On an adjacent street, right next to the Hellenic Seaways office, is a bakery with a bottle-green front, selling particularly delicious savoury pastries. (The potato filo pie, eaten hot from a paper bag while sitting on the bench overlooking the port, becomes a personal favourite.) However, without a doubt the standout feature of Hydra's main town is the not-so-secret swimming spot on the seafront, just past the cannons and underneath the Sunset bar. The water is deep, clear and the particular Pantone shade of blue that you only ever see on Greek islands, shimmering in the sun like a Shirley Bassey sequinned dress under a stage spotlight. I swim there every evening at sunset and there's always a handful of people joyfully jumping off the smooth rocks with the same idea.

My first dinner is at Piato, a traditional Greek restaurant overlooking the water with blue-check tablecloths and walls covered in plates decorated by customers. The menu offers Greek cuisine's greatest hits - stuffed vine leaves and shards of sharp, crumbly feta as well as thick, cool, garlic-spiked tzatziki and a creamy smoked aubergine dip so delicious that I go back for more at lunch. And then a third helping for another lunch, at which point the owner - who has the uncanny twinkly eyed smile of Frank Sinatra - gives me a plate and some Sharpie pens to decorate it with. It now hangs on the wall, alongside the contributions of Kate Moss, Pamela Anderson and Vivienne Westwood. (Incidentally, the food that keeps everyone coming back is thanks to the chef who is, of course, the owner's 80-something-year-old mother.)

Perched above Hydra Town is the Lazaros Kountouriotis historical mansion - a grand marigold-yellow building that's a must-see for architecture and design enthusiasts. The building retains much of the quality of a functioning home from when it was built in 1780, and the ornate furniture, art and textiles are a visual treat that capture the Hydriot opulence of the past. In the basement there is a permanent exhibition of paintings by Constantinos Byzantios, and on the top floor you can peruse examples of traditional Greek dress.

I wandered inland, around backstreets full of bright-white buildings covered in outrageous fuchsia bougainvillea blooms, to reach Vlichos beach. You can also arrive by boat, but the half-an- hour meander through the hills and past Kamini port is a lovely walk. The small, pebbly beach is equipped with sunloungers and the water there is as clear as glass. There are restaurants, and a beachside bar, where the barman is extremely generous with caipirinha measures and kittens curl around your feet. (Cats are quite a prominent feature of the island - they're mostly very docile and often slightly wonky, wandering around like adorable, unloved teddies with one eye or a strangely bent tail.) Just when I think it can't get any more picturesque, a butterfly descends on my forearm, causing me to flap around as though I've just been mugged, only solidifying the frazzled Londoner stereotype.

I walk back along the coast at sunset and the view across the sea and to the west of the island is breathtaking. As I wind round the path, I see a group of artists sitting cross-legged near the cliff edge, sketching the horizon. The walk is peaceful, mainly because there's no fear of a motorbike or a car careering round any corner. Generally, it feels like a very safe place for a woman to travel on her own.

Dinner is a bowl of fresh mussels and orzo pasta on the rooftop of Taverna Gitoniko, where the waiters are vaguely chaotic and a verdant mass of vine leaves covers the bricks. I smile and nod from table to table and notice that I've been wandering around Hydra walking past or bumping into all the same people - the 60-something Australian couple made up of a hippie Billy Connolly and a conservative Janis Joplin pair of lookalikes, the young English honeymooners, the middle-aged German woman who is a fellow solo traveller. A sense of small-island life permeates through the bones of the place - one morning I eat breakfast on the harbour front and watch boats unload stock from the mainland for eager shopkeepers. Another afternoon the sea rages furiously, the piercing wind whistles and the restaurant owners wind in their awnings - one tells me that if the wind comes from the west of the island, a storm is on its way. "But it says no rain today," I say, showing him my iPhone weather app. He shakes his head and tells me that Hydra's weather can only ever be accurately predicted by its weatherman - a man who lives up in the hills who updates his website every day, sometimes forecasting rain at the precise moment that the first drops fall.

Despite the tight community feel of Hydra, I find locating the home of its most famous late resident exceptionally challenging. After three days of saying "LEONARD COHEN?" to locals, in that sort of appalling foreign English accent that embarrassing dads on holiday do, while playing a pretend acoustic guitar, I venture into The Four Corners supermarket on Krieze Street. I have read on online forums that this was Leonard's local shop and before I've even finished the sentence: "Excuse me, do you know where Le-", the wonderfully obliging owner takes me by the arm and points at the tops of some trees down a small lane. "That is his garden," she tells me. "Those grey shutters are his window."

I get to it at dusk, and I am the only visitor there. A candle flickers by his door and the soft late-summer rain (predicted by Hydra's weatherman - I checked) begins to fall. I sit on his doorstep and think of the poetry, songs and stories that he created within those walls; the fleeting and lingering thoughts he had that would become the mantras and mottos of millions. An elderly man shuffles past with his bag of grocery shopping and tells me that he was his neighbour. "Would you like me to take a photo?" he asks, and I feel as though it isn't the first time that he's been so kind.

On my final morning I walk out of the town and hike up the hills just after dawn to visit the Prophet Elias Monastery. The walk takes about an hour and 15 minutes and is challenging, but worth it for the dramatic views across the island to mainland Greece. The brave can mark the peace and serenity of the monastery as a halfway break before climbing up Mount Eros, but I am tempted back to sea level to have a last lunch at the legendary Christina's - a local favourite that looks over Kamini port. It is inconspicuous and far from ashy, but its buttery saganaki, Greek salad and sea view are all delectable in equal measure.

As I board the boat back to Athens and take one last look at Hydra, I make a promise that I'll be back very soon. We have a selfish tendency to want a place to stay just the same when we leave it - like the childhood home that we'll never live in again or the old local pub that we never visit. However, there's something about this island that makes you feel something beyond that longing when you say goodbye - it is so perfect, so set in its ways, that you can't help but hope that the bougainvillea will always grow in the exact same direction, that the lone weatherman in the hills will keep foretelling raindrops. I can see why Leonard Cohen didn't want it to ever change. I don't either.