According to legend, if you look closely, you’ll discover 36 shades of blue in the Aegean. Dotted with 6,000 islands, some big, others tiny, some glamorous, others simple, all have their own myths and history.

No wonder it took Odysseus 10 years to get home — it would be easy to spend a lifetime travelling from one island to another, slowly uncovering their secrets. One island hop is never enough.

My first came after my finals, navigating the erratic timetables of Greek ferries to explore the Cyclades with my best friend, arranging rooms along the way from the old men who waited at each port. My second was distinctly more luxurious, on a cruise from Athens to Italy with my husband, taking me to several new stops in the same island group.

Now this family-friendly country was calling me back again — joined this time by my four-year-old daughter — for a family island hop around the Dodecanese. With a week to explore, our own mini odyssey was limited to two: Kos — one of the chain’s largest and most popular — and Symi, much smaller and less visited but with its own unusual style.

Separated by a 90-minute ferry journey — now distinctly sleeker and more modern than my first hop — the neighbouring pair make a perfect contrast. Better-known Kos is home to bigger luxury hotels, to ancient Greek sites and medieval castle ruins, as well as to golden sand beaches, vineyards and the classic white and blue architecture you’d expect.

Meanwhile Symi, a quarter of its size, could almost have been transplanted from Italy, the blues and yellows of the Roman-style facades sprawling up the hillside above the harbour, small water taxis transporting you to tiny coves around the island. The constant? The warmth of the welcome and the blue of the Aegean.

From our balcony at Lagas Aegean Village near Kardamena in Kos, a hotel attractively designed to look like a traditional Greek village, complete with blue domed viewpoint at the top, we could see yet more islands on the horizon as well as the coast of Turkey. Closer to Bodrum than Rhodes, the biggest of the Dodecanese, you need only visit Kos Town to discover the varied mix of influences that have shaped it over 7,000 years.

Home to a community of Jews since at least Roman times, most emigrated before the Second World War: of those who remained, all bar 10 were sent to Auschwitz in 1943 with only 12 surviving. Today, the post-war synagogue — itself built on the site of an older shul — is used only as a cultural centre.

Phoenicians, Romans, Venetians, Ottomans, not to forget Alexander the Great and Mussolini, all left their mark here too. Within a 10 minute walk of the small synagogue, you can discover a Crusader castle, mosque, Roman temple ruins, Italian fascist architecture and the plane tree of Hippocrates. The island’s most famous son taught students under its shade, or rather more likely an ancestor of the one still standing.

The island’s inhabitants certainly benefited from his wisdom at one of the world’s oldest hospitals too. The Asklepion, dedicated to the Greek god of healing, might not be quite what we’d expect from a medical centre, with dreams used to diagnose ailments, and temples where animal offerings were sacrificed as payment — although the simple healthy diet and hydrotherapy would still get the thumbs up from doctors.

Wandering through the restored site, columns glinting white in the sunshine, the views are enough to leave anyone feeling better. Especially with the news from our guide, Evdokia Zisidou, that Hippocrates considered “wine is the best medicine”.

He did add the proviso that it should be taken with good sense, but a tasting at the award-winning Triantafyllopoulos winery seemed a good place to test the theory — as well as learning that retsina owed its creation to a bottling accident. Discovering the resin seal flavoured the wine, the original makers stuck with it for centuries.

These days the vintages are a long way from that particular acquired taste as we sipped some of the vineyard’s vintages surrounded by its vines, and then other local wines over lunch at a taverna in picturesque hilltop Zia.

With pretty Kefalos to discover too, along with the shallow waters of aptly-named Paradise beach on the south coast plus our hotel’s own pool and patch of sand, the day trip to volcanic Nisyros, an hour off the coast, would have to wait until our next hop. Instead it was time to sail for Symi.

Waving goodbye to Kos, the vines, olive trees and farmland soon turned to drier, rockier islands scattered along the Turkish coast before we pulled into Symi’s spectacular harbour. Once the centre of the sponge diving trade, souvenir shops around the waterfront are still piled high with the genuine article, while tables outside the cafes and restaurants make the perfect place to soak up the views.

Brightly coloured fishing boats bob in the water, their yellow nets as bright as the facades stretching up to the basilica. Gialos, as the harbour known, is the island’s only real centre and home to our hotel Iapetos Village with its small icily refreshing pool, while most of the locals live up the hill in Chorio.

We skipped the 450 step climb between the two for a trip on the island’s bus which traces a circle between the two and Pedi Bay for a couple of Euros, while tours also run to the monastery of the Archangel Michael of Panormitis.

But there’s something in the air in Symi that makes rushing around impossible. Water taxis cruise to little bays, including Ayios Nikolaos where the water is clear enough to see tiny fish swimming along the sea wall. With sunbeds under the trees and parasols against the May sunshine, we moved only to swim and to devour the catch of the day at the little taverna before somehow, the day had passed and the boat was making its return trips.

Then just as quickly, our week was up. Gazing out to the islands from the ferry, two things were certain — I’ve only just begun to uncover the treasures of the Dodecanese, Symi in particular. And I won’t be leaving it quite so long to plan my fourth island hop.