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The haunt of journalists and leading cultural figures, the Gijón was founded in 1888 and is one of the few surviving tertulia cafés where, traditionally, men gathered to discuss issues of the day. Former patrons include the poet Federico García Lorca, the American film director Orson Welles and – more improbably – the famous Dutch spy and belly-dancer, Mata Hari. Order tapas and drinks at the bar or book a table for lunch. The windows look out on to Paseo de Recoletos where the café has its own terrace.

The scale of the Archaelogical Museum’s fabulous collections can be daunting, so home in on what interests you most. The star turn on the main floor is the Lady of Elche , a stone bust of an Iberian noblewoman from the 4th century BC. Other highlights include a Roman mosaic floor representing the months and seasons, the exquisite Recesvinth crown from the Guarrazar treasure (Toledo, 7th-century), a matchless example of Islamic stone-carving from 11th-century Zaragoza, and an ivory processional cross from the church of San Isidoro in León (1063). On the lower floor are Bronze and Iron Age finds from the Canary Islands and a collection of painted amphorae from ancient Greece. Before leaving, take a look at the reproduction of the cave paintings of Altamira on display in the forecourt (see Museo Arqueológico Nacional).

This expansive square, named after Christopher Columbus, commemorates the discovery of the New World. The three monumental slabs near Calle de Serrano were designed by Joaquín Vaquero Turcíos to symbolize the three ships that made the voyage to America in 1492. In the centre of the square is a more conventional sculpture of Columbus, erected in the 19th century. Note a relief on the base which shows Queen Isabel of Castile selling her jewellery to finance his enterprise.

José Lázaro Galdiano (1862–1947) was a distinguished patron of the arts and collector whose Italian-style palazzo is now a museum showcasing his fabulous possessions. There are Spanish works by El Greco, Zurbarán, Murillo, Velázquez and Goya and European paintings by Reynolds, Constable and Gainsborough. There are also spectacular objets d’art (see Museo Nacional de Artes Decorativas).

Situated beneath a road bridge, the open-air sculpture museum is easily overlooked. Nevertheless, exhibited in its windswept precincts are works by a number of outstanding modern Spanish sculptors, including Eduardo Chillída, Julio González, Joan Miró and Pablo Serrano.

One of Spain’s most vital cultural institutions was founded in 1955 by the banker Juan March Ordinas, to promote contemporary Spanish art. Madrid shares the permanent collection, especially strong on abstract artists of the 1950s such as Tàpies, Sempere, Saura, and Millares, with other branches of the foundation in Cuenca and Palma de Mallorca, but the foundation’s main attraction is its outstanding temporary exhibitions (see Real Academia de Bellas Artes de San Fernando).

“Paseo” implies a stroll and this lovely avenue, at its best on a sunny morning or just after sunset, was designed precisely for that purpose. The first cafés began to appear in the 19th century when the boulevard was nicknamed “Recoletos beach”. Most of the originals had disappeared by the 1980s when the Movida gave the terraces a new lease of life (see People and Places of La Movida). The Pabellón de Espejo looks the part with its painted tiles and wrought-iron adornments but actually dates from the 1990s. No. 10 was the residence of the Marqués de Salamanca.

Madrid’s smartest shopping street runs through the heart of the Salamanca district. Here, top Spanish designer names such as Adolfo Domínguez, Purificación García and Roberto Verino, rub shoulders with Armani, Gucci, Yves St-Laurent and Cartier. Even if you’re not especially interested in fashion, there’s plenty to amuse you. Madrid’s best-known department store, El Corte Inglés, has branches at Nos. 47 and 52, Crisol (No. 24) is good for art books, while VIPS Viajes (No. 39) specializes in travel. If you’re looking for gifts, Papelería Saab (No. 20) has a good selection. For a bite to eat, try Serrano 50 which has a menú del día as well as tapas .

This side-street off Serrano has everything from cut-glass decanters to beach bags. For designer clothes for children, try Nanos (No. 21). Vista Alegre (No. 29) has a glittering array of Portuguese-made tableware. If you’re off on safari but still want to look elegant, Colonel Tapioca (No. 32) fits the bill with backpacks, cord shorts, shirts and hats for the fashion-conscious. Estay is just the job for a spot of lunch. Next door but one is Tea Shop (No. 48), with more than 40 aromatic teas, including rum, toffee, cherry and passion fruit.

This museum is devoted to the Valencian artist Joaquín Sorolla y Bastida (1863–1923) who spent the last 13 years of his life here. Some rooms have been left as they were in his lifetime, while others are used to hang his work. Dubbed “the Spanish Impressionist”, his subject matter ranges from Spanish folk types to landscapes, but Sorolla is at his most appealing when evoking the sea. Don’t leave without seeing the Andalusian-style garden.