We’re sitting on the terrace of the café at Kastanis Camping – located between the port of Katapola and Amorgos’ main town, Hora – and gazing down at the harbor. We’re wondering which way the wind is blowing, how many people have disembarked from the ferry, and how many vans and two-wheelers will head past us to the town.

Amorgos is an unspoiled rocky island that offers incredible views of the sea and the islands that surround it. Quietly beautiful, Hora is perhaps the least sophisticated of all the capital towns in the Cyclades. Get anywhere near its renowned traditional coffeehouse, Parvas, and the streets smell of Greek coffee. From Hora, and from the ruins of the Venetian castle up above the town, you get amazing views over the island and out to sea. Some mornings, clouds descend so low here that the horizon disappears in a white haze, and you walk through the mist as if in a dream.

All over Amorgos, small villages, winding roads and stunning gorges invite visitors to explore this island. One of the highlights is Panaghia Hozoviotissa, a blin dingly white monastery that shines out from among the golden-yellow rocks of its cliffside setting. The deep blue sea stretches out in front of it while below lies the small port of Aghia Anna, which is always busy. Here you’ll find two beaches, surrounded by burning black rocks flat enough for sun-bathing and just the right height to use again and again as diving boards.

On Amorgos, you’ll always enjoy great views, even when swimming in the sea. It’s certainly worth heading to Kalotaritissa, a crescent-shaped beach from which a small boat leaves for Gramvousa, a nearby islet. Before you embark, get some homemade cheese pies from the snack bar on the beach. The beautiful clear waters and the complete lack of shade on the sandy beach of Gramvousa will combine to keep you in the water for hours, gazing back at the southwestern side of Amorgos.

The sights don’t stop there: back on land, the winding road to Aegiali offers a bird’s-eye view of the exotic beach of Aghios Pavlos far below; it consists of a strip of land that has somehow resisted drowning in the turquoise waters that lap at its edges. From Tholaria above Aegiali, it’s a one-hour walk down to the path to dreamy Mikri Vlychada Bay.

The route is largely shadeless but it offers glimpses of the wild beauty of the Cyclades, where drystone walls, thorny scrub plants and bristly grass prevail. The path is fine for people who are comfortable walking moderate distances, but if you do find the descent to the bay hard, note that you’ll have even more trouble on your way back up the path. For those who make the trip, however, the effort is worth it: you’ll find a small sheltered beach flanked on both sides by low cliffs and washed with cool refreshing waters. Not too far out from the narrow shore, this small inlet opens onto the wide sea. After your swim, head back to the tidy whitewashed settlement of Tholaria to enjoy one of the Cyclades’ quietest sunsets.