Beach holiday. Sand optional

It is early evening in the Mediterranean, the time when the warm sun and cool breeze each struggle to gain the upper hand. Look one way and you gaze into an endless sea; look the other to see a Gothic cathedral rising above the palm trees, its mellow sandstone turned to gold by the last of the sun. This is the scene as you stand on the seafront in Palma de Mallorca.

Go to any airport this summer and you will find flight after flight heading for Palma. A million Britons fly there every year and most make straight for the beaches, which begin just minutes from the airport. The 15-mile stretch of the Bay of Palma has more tourist beds than the whole of Greece. Yet in the middle of all this is a sublime city that few tourists bother to visit - a smaller, sunnier version of Barcelona right down to its Catalan street names and its rambla lined with flower stalls. And thanks to the package holiday industry you can go there a lot more cheaply than to Barcelona.

The cathedral by the sea dominates all else. Begun in 1230 on the site of the city's Great Mosque, it served as a reminder to all who arrived by sea of the might of Mallorca's Christian conquerors. The building of it took almost 400 years and more touches were added this century by the Catalan architect Antonio Gaud. His crown of thorns, suspended above the altar and fashioned from cardboard, cork, nails and brocade, needs to be seen illuminated. Join a large congregation for the Sunday morning Mass.

Next door is the royal palace whose Moorish arches, lit up at night like a row of lanterns, speak of Mallorca's Arab past. A thousand years ago, while other cities were in the Dark Ages, Palma (then known as Medina Mayurqa) had street lights, covered sewers and heated baths. The tiny Arab Baths are all that remain, and sitting in the courtyard, shaded by cactus, palm and orange trees, you can imagine yourself cooling off after a spell in the hammam.

It is easy to get lost around here in the maze of narrow streets, each just wide enough to take a car. Enormous wooden doors hide patios of stone steps, balconied arcades and ancient wells. Palma's former palaces have been turned into apartments, while a few have become stylish hotels.

When you tire of history, head for the suburbs and the house and studio belonging to the painter Joan Mir. Mir spent most of his life in Barcelona, but his wife and mother were Mallorcan and he always longed to return to the scene of his childhood holidays. In his paintings he used bright splashes of primary colours in conscious imitation of Mallorcan peasant pottery. His studio has been left untouched since his death in 1983, with work on the easels and open tins of paint.

A generation of Mallorcan artists has grown up inspired by Mir, and Palma has become an important centre of modern art. Of several galleries, the most interesting is La Llotja, the 15th-century maritime exchange on the seafront. Half-castle, half-church, with twin turrets and an angel over the door, it would be worth a visit just to see the finest rib-vaulting in Mallorca, but there are also changing exhibitions of contemporary art. This is the best value visit in Palma - it costs absolutely nothing.

Near here is the start of Passeig Martim. A promenade and cycle path follow the harbour around to the Club de Mar, where you look back towards the cathedral through a forest of masts and fishing-nets. The walk is best done in the evening, the traditional time for a paseo; as dusk turns to darkness, the cathedral lights up and Passeig Martim becomes the fashionable place to dine. At S'Arrosseria the speciality is rice, cooked in a dozen styles from vegetarian "convent rice" to a full-blown lobster paella. Second helpings are the norm.

Celler Sa Premea, at the other end of town, is lined with massive oak vats and faded bullfighting posters. Wine comes out of a tap in the wall and the menu features Mallorcan classics like frit, a fry-up of offal, potatoes and tomatoes in olive oil. Go before 10pm and it will be packed out with tourists; go late if you want to see how the locals eat.

To find out what you're missing, take the bus one night to Palma Nova. This brash resort was once a mere village - someone who grew up there in the 1950s told me that he went back recently and only recognised one building. The menus are in English and feature local specialities like beans on toast; the bars serve John Smith's (lots of them) and do their bit for sobriety with offers like "a baseball cap with every two pints of sangria".

Take the last bus back to Palma and head instead for Abaco, a restored 17th-century palace turned into a pleasant bar near La Llotja. You sit on a sofa surrounded by antiques, sipping cocktails by candlelight to the sound of classical music and the scent of incense and fresh flowers. Palma Nova is less than ten miles, but it could be a world away. Order another drink and give thanks that you decided to stay in Palma.

Getting there

Iberia (0171-830 0011) and British Midland (0345 554554) both have scheduled flights from Heathrow to Palma from pounds 160 return in May. Thomson (0171-707 9000) and numerous other companies operate charters from all over Britain - the author paid pounds 75 return from Stansted in February.

Where to stay

Hotel San Lorenc, Carrer Sant Llorens. 14 (00 34 71 728200); doubles around pounds 85. Hotel Bornes, Carrer Sant Jaume 3 (00 34 71 712942); doubles from around pounds 47. Both are converted palaces in the old city.

Where to eat

S'Arrosseria, Passeig Martim 13 (737572); Celler Sa Premoa, Placa Bisbe Berenguer de Palou (723529); Caballito del Mar, opposite La Llotja (721074) for expensive seafood.