Most Greek islands shut up shop from October to April — hotel doors close, beach bars are dismantled and only a handful of tavernas remain open to feed the small local population. But some islands really come into their own after the summer heat and crowds simmer down. The largest, including Crete, Corfu and Andros, are not solely reliant on tourism. Their valleys and hills are full of sheep, farms and sleepy villages, while seaside towns thrum with students, live music, and buzzy cafés all year round.

There are plenty of smaller islands whose charms also run deeper than dazzling coastlines — from unsung archaeological sites to arts festivals, food markets and extraordinary architecture. And, while accommodation options are limited, off-peak prices can be half what they are in high summer. Greek winters tend to be mild, although winds can be fierce — so fierce that ferries are occasionally suspended and you might get stranded on islands without an airport. But really, the prospect of an extended stay is just another good reason to explore these enchanting isles off season.

1. Aegina

Only about an hour’s ferry ride from Athens, Aegina is sometimes dubbed “the commuter island” by locals. That doesn’t make this lively, unpretentious island any less charming. The harbour is a pretty picture of bobbing boats, fish tavernas (Skotadis is the standout), and fine-boned mansions in varying degrees of disrepair.

While here, uncover unexpected treasure hidden among the weekender clichés: time-warp kafenia (cafés) clustered around the fish market, a plateau of ancient olive trees protected by a ridge of stony hills, Byzantine chapels camouflaged in acres of blush-pink pistachios, the island’s most famous export. The striking archaeological sites of Aphaia and Kolona are bizarrely underrated; outside July and August, you can often enjoy the ruins in meditative solitude.

Aegina’s beaches aren’t brilliant — which is exactly why it’s an excellent off-peak destination — but there are rocky inlets where you can plunge into the luminous sea without freezing half to death, even in midwinter.

Where to stay Nikolaou Residence, the former home of Greek painter Nikos Nikolaou, is now a three-suite guesthouse full of art, antiques, and class on a peaceful stretch of seafront.

2. Syros

In the middle ages, Venetian crusaders ruled Syros and established a Catholic settlement that still crowns the unorthodox capital of the Cyclades. By the 19th century, enterprising refugees from Asia Minor had transformed this modest trading post into a flourishing industrial and shipping centre.

This legacy is very much evident in the neoclassical port capital, Hermoupolis. The administrative centre and university town is urbane and cultured without a trace of touristy artifice. Throughout the year, expect a calendar full of street parties, arts festivals and religious celebrations (on Twelfth Night, the boats in the harbour set off flares, a fantastic spectacle). Locals get together over mezze and live music in cosy bistros and bars, such as the atmospheric Cantina Analogue and Laoutari, or venture into the vast nature reserve in the northern hills to forage for herbs.

Non-profit outfit Hermoupolis Heritage brings behind-the-scenes glimpses of the island’s illustrious past — a night tour of an abandoned textile factory, a picnic in a crumbling country estate, or a gentle cruise on a beautifully restored wooden caique.

Where to stay Hotel Aristide, a historic mansion that combines lavish style, strong eco-cred, and an excellent location in Vaporia, the handsome shipping quarter of Hermoupolis. Book several months ahead for off-season stays.

3. Crete

So far south it separates the Aegean from the Libyan Sea, Crete has a temperate climate that makes year-round swimming a tempting, rather than terrifying, prospect. Photogenic beaches such as Balos, Elafonisi, Vai and Preveli are even more appealing without the summer crowds, while snow-capped peaks and deep canyons provide challenging terrain for hikers, climbers and mountain bikers. Basic but brilliant taverns in hillside villages serve fortifying lunches of roast goat, lamb pilaf and bracing shots of raki, the grape distillate that is knocked back at every opportunity.

And of course, there’s a whole Minoan civilisation to explore: Knossos, Phaestos and Malia are a different world without the coach and cruise parties. Then there are the Roman ruins, Byzantine monasteries and Ottoman monuments. As the 19th-century British satirist Saki wryly noted: “The people of Crete unfortunately make more history than they can consume locally.”

Where to stay A cosy stone cottage at Kapsaliana Village Hotel, an 18th-century village set in the island’s largest olive grove.

4. Corfu

Evergreen Corfu is coming into its own as a year-round destination. Mass tourism has blighted much of the coastline, but swathes of the interior have hardly changed since the Durrells fell for its magic, which “settled over us as gently and clingingly as pollen”.

The 136-mile Corfu Trail runs the length of this lush island, weaving through juniper forests, lakes, gorges and vast expanses of olive trees (four million and counting) planted by the conquering Venetians centuries ago. Their Italianate influence is present everywhere: in comforting dishes such as pastitsada (macaroni with rooster), in stone villages such as Perithia and especially in Corfu’s Venetian Old Town.

Tourist traps close in winter and locals return to the marble-paved alleys for sophisticated tapas at Salto and snazzy cocktails at Mikro Café. Perhaps the most unspoiled corner of Corfu is the Erimitis peninsula, an area of incredible beauty and biodiversity.

Where to stay Choose from two sunny, stylish cottages in a hundred-year-old olive grove on Dr Kavvadia’s organic farm, just outside Corfu Town. Guests can join the olive harvest (October and November), raid the kitchen garden and chicken coop, or sign up for relaxed food and wine workshops.

5. Andros

Unlike most of its Cycladic neighbours, Andros is exceptionally green, incredibly diverse, and almost disdainful of tourism. Even in summer, most visitors are Greek and the mist-swirled peaks and dirt tracks that peter out at untouched beaches never feels crowded.

Chora, the capital, juts purposefully into the Aegean, its stately mansions, museums, and municipal buildings a legacy of the local shipping fortunes amassed in the 19th century. Hippies have settled in the tiny hilltop hamlets; bohemians host dinner parties in lavish country piles inherited from their ship-owning ancestors; and in the hinterland, life goes on pretty much has it has for decades. Farmers still please passing ramblers with freshly churned goat’s cheese and jars of preserved fruits; the wetlands rustle with migrating birds and impenetrable forests chime with freshwater springs. Andros Routes is an excellent resource for self-guided walks along the island’s many waymarked trails.

Where to stay Citrus Orchard Estate, a tactfully modernised 150-year-old country house in the lush plain of Livadia. A hiking trail passes by the property, which comes with five bicycles and a pool for warmer days.

6. Rhodes

As one of the most southerly Greek islands, Rhodes benefits from a relatively long summer season, which typically extends into November. But even in the winter months temperatures tend to be mild, and there are a growing number of hotels staying open all year round to help those in the know take advantage of this.

The medieval Old Town is the most obvious place to start. A Unesco world heritage site, this fortified city was established in 1309 when the knights of St John made their base on the island. Today, its cobbled streets are pedestrian-only, perfect for strolling past those grand townhouses at leisure.

The port of Mandraki is another essential stop for history. Here you’ll find the spot where the 108ft high Colossus of Rhodes once guarded the island, before it toppled into the sea after an earthquake. Then there’s Lindos in the south, a petite village dotted with whitewashed buildings built into the hills and its own acropolis surveying the picturesque scene.