10 fabulous Greek islands that should be on your radar

1. Alonissos

West of its better-known big sisters, Skiathos and Skopelos, Alonissos sits within a unique marine conservation area, amid a cluster of tiny uninhabited islets that you can visit by boat.

Gentle green hillsides are great for easy-going island walking, and at Agios Dimitrios and Kokkinokastro, you'll find glass-clear water and clean pebbles. The big deal here for scuba divers is Greece's first underwater archaeological museum, centred on the wreckage of a 2,500-year-old cargo vessel called Peristera, where thousands of ancient, barnacle-encrusted wine amphorae lie scattered on the seabed.

Patitiri, the island's port village, is still authentically Hellenic, with plenty of cheerful café-bars and restaurants. Wherever you go on Alonissos, you'll find welcoming locals outnumber visitors. That’s no bad thing.

How to get to Alonissos: Fly direct from the UK to Skiathos, then jump on a 95-minute high-speed ferry to Patitiri.

2. Andros

There's plenty of room for all on Andros. At 380 square kilometres, it's a biggie, but there's no airport, which has kept the brakes on international tourism.

If you're expecting an island capital that's all whitewashed houses and narrow winding lanes, Chora will surprise you. It's a gracious little town of neo-classical townhouses, built by the well-off shipowners who dominated here in the 18th and 19th centuries.

Car-free Plateia Kairis, the café-filled central square, feels a bit like Athens as it used to be – which may be why Andros is so favoured by Athenians taking their summer break from the capital's chaos. Down a set of stone stairs to sea level, Chora has its own beach at Paraporti.

The island's main beach resort is Batsi, a one-time fishing village on a long crescent of yellow sand. Andros is also a cracking island for walkers, with easy walks on old country paths among gently rolling hills dotted with medieval monasteries and Venetian dovecotes.

How to get to Andros: Fly to Athens, then take the ferry from Rafina, about 20-30 minutes from the airport. The boat trip takes just under two hours.

3. Evia

Is it an island – or isn't it? Technically, Evia is Greece's second largest isle (after Crete) but you don't have to hop on a boat to get here. A road bridge connects it to the mainland at Halkida, midway up the west coast, so you can drive straight there from Athens International Airport in just over an hour. That's a bonus for families who need a hassle-free island break, and for road trip ready explorers.

And there's plenty to explore on Evia. Looming above Karystos, Evia's main ferry port, 1,389m (4,585ft) Mount Ochi offers a challenge for energetic walkers, and its slopes are scattered with mysterious ancient 'dragon houses' (drakóspita) built more than 2,500 years ago.

For the best beaches, stay at Mourteri, on the east coast, Agia Anna near the northern tip of the island, or Chiliadou, a 75-minute drive from Chalkida.

There's good eating in traditional restaurants all over the island, especially in Chalkida, Karystos and the pretty, peaceful 19th-century harbour town of Kymi, on the east coast.

How to get to Evia: The drive to Halkida takes around 75 minutes from Athens International Airport, or you can take a 60-minute ferry from Rafina.

4. Ithaca

There's more to the Ionian Islands than crowded Corfu, rowdy Zante or big-but-sleepy Kefalonia. If you've had your fill of these, hop on a boat to Ithaca, home of Trojan War hero Odysseus. Here, you’ll discover a different kind of Ionian haven, where boutique hotels and authentic island tavernas gather around the secret harbour at Vathi, set on a deep blue fjord.

Ithaca's beaches are pebbly and scattered around the hourglass-shaped island's coasts – jump on a water taxi to Kioni for the best beaches or stay here in one of an assortment of budget-friendly small hotels and apartments with shared pools.

This isn't an island for party animals, but for couples looking for somewhere to decompress for a week or two, Ithaca is hard to beat.

How to get to Ithaca: Fly direct to Kefalonia, then take the 30-minute ferry from Sami (at least three daily).

5. Kythira

According to legend, Kythira is the birthplace of Aphrodite. That's appropriate, because this is a dreamy island for romantics. Chora, the island capital, is a maze of narrow whitewashed lanes huddled around a 16th-century Venetian citadel and perched high above the double bay of Kapsali with its half mile of sandy beach, clear water and clutch of harbourside cafes.

There are more beaches scattered around Kythira's coast. Some of them are hard to get to without your own transport but Diakofti, the island's northern harbour village, has a stretch of white sand that’s worth making time for.

Kythira's plateau-like hinterland rewards walkers with valleys and gorges where you can swim in waterfall pools, and sleepy villages like Mylopotamos with tavernas set around squares shaded by plane trees. For a day out, take a boat trip further afield to the island’s little sister, Antikythira.

Places to stay on Kythira include a handful of upscale small resort hotels with pools, boutique hotels in restored old mansions, and self-catering apartments.

How to get to Kythira: You can fly from Athens to Kythira in under an hour or take the four-hour ferry from Kissamos in Crete. There are three sailings weekly.

6. Kythnos

Greece's best-loved trail, the Samaria Gorge on Crete, is a crowded cavalcade of walkers all summer. Get away from the thongs on Kythnos, a well-kept Cycladic secret, where cobbled donkey trails criss-cross a landscaped of terraced fields, olive groves, windmill towers and little villages of boxy, whitewashed houses and blue-domed churches.

At the end of a day's hiking, you can ease aches and pains in the natural hot springs at Loutra, on the north coast, and there are small, crowd-free beaches at Episkopi and Apokrousi, and around Kanala.

Kythnos is also a paradise for birders and other nature lovers – its hillsides are splashed with colourful rare orchids and fritillaries in spring, and it’s visited by flocks of migrant birds in spring and autumn.

Nightlife isn’t rowdy and you won’t find big clubs, but there are a couple of music bars in Merihas, Kythnos' main harbour village, where you'll also find good seafood restaurants.

Most accommodation is in simple guesthouses in Chora, the island's tiny main village, and at Loutra.

How to get to Kythnos: There’s no airport on Kythnos so aim for one of the three weekly sailings from Piraeus, Athens’ port city. Journeys take about three hours.

7. Milos

For otherworldly scenery, Milos gives its Cycladic sister isle Santorini a run for its money. Here, though, the colour scheme is stark white, splashed with red, set against turquoise sea.

At spots like Sarakiniko, weather has sculpted Milos' soft volcanic rock over millennia, but some of its weird landscapes are the result of centuries of quarrying for sulphur and manganese.

Milos is brilliant for beaches, too. Some, such as Achivadolimni, Agia Kyriaki and Fyriplaka, come with beach bars, loungers and umbrellas. Others, like Alogomandra and Triades are delightfully undeveloped.

As for where to stay, Adamas, Milos' port village, is full of cafes and tavernas while Apollonia is a friendly low-key resort on a tree-lined beach. You won't find any big hotels on Milos, but there's a growing portfolio of chic boutique hotels and guesthouses, and plenty of apartments with shared pools.

For something unique, stay in a converted syrma. These brightly coloured pads were originally used as boat sheds but today, many have been converted into cool summer hideaways where the sea is literally on your doorstep.

How to get to Milos: Flights from Athens to Milos take around 40 minutes; ferries from Piraeus are longer (between three and six hours).

8. Naxos

Naxos isn't exactly a well-kept secret. It's hard to hide the largest island in the Cyclades, one that’s five times the size of Mykonos. But for some reason it never grabbed the imagination of the mass tourism business.

Naxos has plenty going for it, though. Naxos Town is a lively community that hasn't yet been entirely gentrified and has plenty of buzzy cafés and tavernas. And hidden away in its historic Kastro district are a splendid palace and grand mansions dating from the medieval era, when this was the capital of the Venetian Sanudo dynasty.

Beach lovers will find plenty to please them on Naxos' west coast, with long sandy beaches at Agios Georgios, Agia Anna and Plaka.

How to get to Naxos: Jump on a ferry from Piraeus (fastest journey 3hrs 25 mins), Mykonos (40 mins) or Santorini (1hr 30 mins). Or, fly from Athens to Naxos Airport Apollon.

9. Paros

Think of Paros as Mykonos without the oligarch-style excess. It's a short ferry ride from its high-profile neighbour, but it seems a world away.

Still, the smart money is tipping it as 'the next Mykonos', and it's easy to see why. It ticks all the right boxes, with whitewashed, sugar-cube villages, tiny, blue-domed Orthodox churches and uncrowded golden beaches.

Head to Chrisi Akti on the southeast coast for family-friendly sands and world-class windsurfing and kiteboarding.

Island capital Paroikia (where your boat lands) hits just the right note for nightlife – lots of authentic tavernas and lively bars that haven't (yet) been taken over by Kardashian wannabes.

Naoussa, on a bay on the north coast, is a cluster of white houses around a pretty harbour and some surprisingly cosmopolitan places to eat and drink.

If Paros itself isn’t far enough off the beaten track for you, hop on the boat to its tiny sibling, Antiparos, with its plethora of crowd-free sandy beaches.

How to get to Paros: It’s a 45-minute ferry ride from Mykonos or Santorini, or a 45-minute flight from Athens International Airport. A new airline, Fly Clycladic, based in Paros, has flights from Mykonos, Santorini, Rhodes and Crete (all of which have direct flights from the UK).

10. Patmos

The last three digits of the Patmos tourist office's phone number are 666, which is spookily appropriate, because the Cave of the Apocalypse, where St. John the Divine composed the Book of Revelation, is this craggy island's big ticket. It's within the fortress-like Monastery of Agios Ioannis, crouched on a hilltop and surrounded by the white houses and narrow lanes of postcard-pretty Chora, high above Patmos' port village, Skala.

The Greek Orthodox Church's conservative influence has kept tourism low-key here (they're very down on nude sunbathing), but Patmos has more than 20 beaches of clean sand and pebbles. Biggest and most popular is family-friendly Kambos.

Around four miles from Skala, it's the nearest thing Patmos has to a resort, with watersports including water-skiing and windsurfing. You can explore the others, including gorgeously remote Psili Ammos, using water-taxis from Skala.

How to get to Patmos: Fly to Kos direct from the UK, then take the daily ferry (2 hrs 30 mins) to Patmos.