In May it is bliss, silent except for whistling bee-eaters: Tinos, the Cyclades, Greece | Greek Islands holidays

We are staying in the House of Light (from £62 a night, £90 in summer, sleeps three, on Airbnb), which is a work of art where even the shower drains through locally handcrafted ceramic. I pad along barefoot to the terrace and sit down on the stone bench in the sun, looking across a field of daisies, poppies and mallow to the crumbling dovecote.

As with all the villages of Tinos, Kato Klisma is busy in the summer months, says our host, but in May it is bliss; silent except for whistling bee-eaters. If I walk down one nearby alley, the croaking of frogs leads to a maze of bamboo-encircled fields where sheep graze on artichokes. The valley stretches to Kolymbithra, a sweep of white sand drifting up to blue cliffs, backed by dunes and lagoons populated by ducks and wading birds.

Beyond are a couple more beaches with laid-back cafe-bars. Deeply relaxed after quiet hours by the sea, I walk back while admiring the golden glow of the grassy hillsides and the swallows flitting around me. Then it is up the hill to the village of Aetofolia (eagle’s nest) for a taverna dinner: mushrooms in garlic and fresh parsley, beefburgers with mint, fresh-cut chips and springy bread, and a slice of halva on the house.

Unlike its smaller but much busier neighbour Mykonos, Tinos is known for quiet pursuits: in particular, a church that pilgrims approach on hands and knees to ask or thank the Virgin for miracles. It’s also known for beautiful villages spread across the hills, and the network of stone footpaths that once linked them.

At Loutra, a short distance from the bare granite peak of Exombourgo, is an Ursuline monastery where, in the 1880s, Englishwoman Mary-Ann Leeves ran a girls’ school, having the pianos she had ordered brought by mule up the steep paths.

Naturally, things have changed a little since then, and most people rent a car at the harbour. A well-heeled clientele now enjoy stylish villas and boutique village hideaways blending luxury with tradition, and eat at restaurants offering modern cuisine and high-end wine lists.

Well-heeled in a different way, we set out to explore the captivating natural beauty of the island on foot: there are hills deeply etched with old terrace walls and lush valleys dotted with dovecotes dating from the days when the birds were bred for meat and natural fertiliser. Prosaic as their origins were, they are like palaces for pigeons, each tower uniquely decorated with geometric shapes.

The dozens of elegant villages often have tongue-twisting names – Ktikados, Smardakito – and blue church domes with intricate belfries, their designs influenced by the centuries of Venetian rule. Houses are jumbled together in an abundance of prettiness, impenetrable to cars; there are walls thick with white plaster like cake icing, carved marble arches over door and windows, potted plants and gushing springs.

There are also empty hillsides and unspoilt beaches. From the village of Potamia, where our host brings us filo rolls with honey and cinnamon, I walk past chapels and grazing sheep to Santa Margarita, a beach with gentle blue-green pebbles.

Another day, heading towards Ayios Romanos beach on the other side of the island, I veer off our route to discover an arc of fine, pale sand shelving into shimmering sea, with a backdrop of wild bushes and old stone ruins on a hillside.

I visit the village of Komi as it is preparing for its annual artichoke festival, the square lively with chatter. We drink cold organic Nissos beer from the local microbrewery with a meze of bruschetta topped with juicy tomatoes. As dusk falls, we pass hefty cattle settling in the fields, milk cans at the roadside and falcons circling above old windmills.

At a taverna run for more than 20 years by Mathios, we enjoy steaks, salad heaped with capers and cheese, and wine for a few euros a carafe. We later walk home under the stars, listening to the peeps of scops owls.