Hydra is where well-heeled Athenians go for weekend breaks. It’s what Long Island is to New Yorkers, or Île de Ré to Parisians.

For, while Corfu is a 12-hour ferry ride away and Santorini six, Hydra can be reached in as little as 1hr20 on the regular scheduled boats out of Athens. And – unless you own your own yacht – there’s no other way to get there: there’s no air or heliport, there aren’t even any cars.

We tacked a day trip to Hydra onto a weekend city break that was otherwise full of the classical antiquity you'd associate with Athens. Greece's capital has, in the Acropolis and sister sites, arguably the greatest tourist attraction in the world but it’s not the easiest city to negotiate and tends towards the frenetic: it has a population north of three million, most of whom at any one time seem to be talking loudly, whereas Hydra’s permanent residents number barely 2,000 and are altogether quieter.

The city’s port, Piraeus, a few stops from central Athens by metro, is also historic in its own right – it was from here that the Greek fleet set off to defeat the Persians in the battle of Salamis in 480BC – though these days it’s less a tourist stop than a hub of global trade and industry, a chaos of modernity.

But as soon as the Hydra passenger ferry leaves the harbour wall, the day descends into calm: hectic Athens and Piraeus are left behind and you’re out in the tranquil Aegean, which is millpond flat and deliciously blue.

The ferry heads south and west between the meandering mainland and a series of small islands: Aegina, Methana and pretty Poros – where it briefly stops – before rounding a headland and making across the final channel to Hydra itself and into the port of the island’s only town.

Before you’ve even docked you have seen it all: the steep elevation away from the water with white-walled, red-roofed houses rising at rickety angles in every direction.

And this is basically it. You might be tempted to call it a one-horse town were it not for the fact that what greets you as you step down the boat’s ramp onto the harbour-side is quite a number of horses – and an even greater number of donkeys. These are the only means of transport apart from shanks' pony.

Which brings us back to the lack of cars. Hydra is made up of narrow alleyways so steep and bumpy that it’s not just cars that are absent but bicycles too. This is quite the antidote after a stay in traffic-choked Athens and has a soothing effect on the pace of life.

There are a few sights: a quite charming small cathedral dating from the 1650s, numerous churches – black-clad priests passing are a common sight – a parochial museum, some gnarly cannons on ramparts pointing at invaders arriving by sea like ourselves. But there’s only one that’s known more widely: ‘Cohenhouse’.

Leonard Cohen spent a few bohemian years here as an unknown poet in the early sixties before picking up a guitar and finding international fame as the miserablist troubadour providing the soundtrack for a million bedsit broken hearts. And so became the island’s most famous son.

To find his house you can ask any local for ‘Cohenhouse’ and they will point you up the next alley to another local to ask until you find it. It’s not much: a modest whitewashed stone house with walled courtyard garden differing little from its neighbours except, no doubt, in the amount of marijuana that’s been smoked outside it over the years in homage to its famous resident.

And that really is the tourism done. For dinner, we pick from the restaurants that surround the harbour and choose the one that seems to have the freshest fish. The patron produces a tray of his wares on ice and claims to have caught them himself this morning. I initially dismiss this as patter but after a prolonged discussion about sea bream varieties and habitats it’s plain from his expertise that he’s telling the truth.

Our lunch becomes a spectacle observed by quite a number of cats. The whole town is teeming with them; the odd missing eye or gouged ear an indication that their life isn’t always easy as their dozy habits suggest.

After lunch we walk beyond the town to see more of the dramatic landscape of steep dark stone hills softened by the occasional pine tree and numerous charming rocky coves with the water as clear as you could wish; temptingly clear. I see some stone steps leading down to the water’s edge and find myself following them down and in. It’s fresh certainly but relatively warm for early spring and delightfully cleansing after Athens. As I return to town, hair dripping, I get a glance or two suggesting that swimming before Easter may be seen here as eccentric. But these Hydrans are plainly not listeners of Radio 4, leading global promoter of all weather ‘wild swimming’.

We repair to the harbour bars where an ouzo restores full body warmth and we watch the dozing cats some more.

The nearby newspaper rack points to Hydra's many metropolitan escapees: there are copies of The FT, The Daily Telegraph, Le Monde, La Republica, The New York Times.

As we wait to board our boat back to the bustle of Athens we pet the donkeys. They’re waiting to see what new loads they will be given from the arriving boat. And we watch them having sheets of roof insulation, a washing machine, even a wardrobe roped onto their backs.

A local superstition dictates that a coin thrown into Hydra’s harbour as you depart ensures you will be back one day. We duly toss silver into the water.

John Sturgis is a veteran Fleet Street news journalist