Why should I go? This year, 9m people will fly to Mallorca. The good news is that 8,999,998 of them will head straight for the beaches, leaving you free to enjoy a compact collection of museums, galleries, restaurants and suave hotels.

What do I do? A stroll along the waterfront gives you the best view of La Seu Cathedral — a central landmark, with the old city arranged around and behind it. Built in the French-Gothic style, it’s huge, with an altarpiece and giant candelabras by Gaudi. Construction was started in 1230, but the main part of the cathedral was not finished until 1601 and the bell tower remains incomplete today. Builders, eh?

Palma’s architecture is a mishmash of two things: the mini-baroque, and flat-fronted Catalan houses, their wrought-iron balconies facing each other across narrow streets. And there’s still evidence of the Moorish occupants, ousted in the 13th century, in the form of the Arab baths.

Es Baluard museum, home to modern photography, ceramics and paintings (www.esbaluard.org), is pretty spectacular to look at, too —it was created by adding stark concrete walls to the remains of Palma’s 16th-century ramparts. It has an excellent restaurant, Es Robost d’Es Baluard, serving new Mallorcan cuisine (9 Plaça Porta de Santa Catalina; 00 34-971 719609; £24pp).

Also worth a look is the March Foundation (www.march.es/arte/palma), which houses 70 permanent works as well as frequent temporary exhibitions, featuring mostly modern Spanish artists.

But if you’re the kind of philistine (like me) who thinks that the best souvenirs come in 100% cashmere, make for Jaume III, one of the main shopping broadways. From there, go south, for the modern Spanish giants Zara and Massimo Dutti, as well as interesting little boutiques.

Where should I eat? Go straight to La Boveda, a noisy and authentic tapas bar on Carrer Boteria (971 714863). For those really in the know, there’s Bar España, at the corner of Carrer del Bane and Calle de Can Escursac, farther up the hill into the old town (no telephone — and beware, they stop serving tapas at 10pm).

For fancy-pants dining, try Restaurant Parlament (971 726026, www.restaurantparlament.com), next to — unsurprisingly — parliament, all columns, mirrors and chandeliers, with wonderful paella (£9).

Where do I stay? If you’re into posing in rooftop pools and flopping on four-poster day beds, try the Puro Hotel (www.purohotel.com; doubles from £173). It also has a private beach, a short taxi ride out of town, with massages and yoga (Cala Estancia, Can Pastilla; 971 744744).

For true sanctuary, Hotel Convent de la Missio (www.conventdelamissio.com; doubles from £156) is a converted convent building in the old town, with a more ethereal vibe. More modest, but still occupying a grand 16th-century palace near the cathedral, is the Hotel Born (www.hotelborn.com; doubles from £64), which has large rooms, some antique furnishings and breakfast outside on the patio.

How do I get there? There are flights to Palma from 22 UK airports. Airlines include Jet2 (0871 226 1737, www.jet2.com), bmibaby (0871 224 0224, www.bmibaby.com), easyJet (www.easyjet.com) and Monarch (0870 040 5040, www.flymonarch.com). Aer Lingus (0818 365000, www.aerlingus.com) flies from Dublin.

— Chris West travelled as a guest of the Spanish Tourist Office (020 7486 8077, www.tourspain.es)

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