Mention that you’ve been to the Azores and most people in Britain will nod knowingly, then, after an acceptable pause, inquire tentatively: “Where are they exactly?” Without getting into longitudes and latitudes, the volcanic archipelago lurks out in the middle of the Atlantic, a little more exposed than the better-known winter sun resorts of the Canaries or Madeira.

When you hear that they are volcanic, you expect the dusty, grey, sun-blasted aspects we associate with the Canaries, but instead the Azores feel like little chunks of rural Portugal chipped off and hauled into the middle of the ocean.

Substantial rainfall and powerful winds keep them lush and verdant, while the main industry — dairy — means the green fields are invariably dotted with cattle chewing the grass.

Unlike the other Atlantic island groups, tourism has yet to make a substantial impact on the islanders’ way of life, and for now most visitors to the Azores seem to like it that way, falling mostly into the retired category, here to enjoy the countryside rather than live it large in happening nightclubs (not that there are any).

Most international flights arrive at Ponta Delgada on the island of São Miguel. It’s a misleading first impression, being (almost) a city, with a little urban scruffiness and a swathe of new housing going up on the road to the airport.

However, in the centre it is an elegant Portuguese town, all 17th- and 18th-century baroque frontages, airy squares, and evidence of the importance of Ponta Delgada as a stop-off place for the ships bringing back the riches of Brazil to the homeland a couple of centuries ago.

If Ponta Delgada provides a diverting day wandering from church to square, on São Miguel the main attractions lie east and west, easily attainable on the slow but regular buses from the capital.

The most photographed vista in the Azores is the view from Sete Cidades, in the northwest of the island. Here, two lakes merge, but by some geological marvel one appears blue, the other green. It’s a stiff 7Å-mile walk around the ancient volcano caldera that holds the lakes, and Atlantic breezes invariably blow in clouds to obscure the view.

From Sete Cidades, a path over the ridge of the crater eventually leads down to the coast and Mosteiros. The fishing village has a relaxed atmosphere, some cheap and attractive cafes, and an air of having been unchanged for a century or so.

The sea walk gives you as bracing a taste of the Atlantic breeze as a stroll in Troon and justifies a slap-up lunch in the Restaurante Barbosa. Locally caught fish is the attraction, washed down by a jug of the island’s vinho do cheiro, a robust red with a piquant floral flavour.

To the east lies Furnas, famous with 19th-century travellers as a spa town, and still dramatically punctuated by churning volcanic springs. Above the town by the Furnas lake, local restaurateurs take advantage of the hot volcanic soil to slow-cook the region’s signature dish, cozido nas caldeiras, a hearty meat and vegetable stew.

São Miguel is the largest of the eastern islands. The central group have a subtly different feel. São Jorge, a long thin sliver of an island, with a high crest separating north and south coasts, is ideal for walking.

Its main settlement, Velas, is a sleepy, some might say soporific, village, architecturally similar to the “white towns” of the Andalucian mountains, although the climate is more reminiscent of Brittany.

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