Madrid sprouted suddenly out of a little-known 16th-century backwater after Philip II decided it would make a good capital. This gives it a rather grand architectural coherence, and, with city walls that only fell in 1860, it also has a remarkably compact old town. This is where you’ll find most of its government buildings, major cultural institutions, restaurants and nightlife. Madrid has three reference points: the Puerta del Sol, the city’s absolute centre; the Plaza Mayor, the Golden Age core; and the glorious Plaza de Cibeles, with the most extravagant architecture.

The big three are getting bigger – the Prado, Thyssen and Reina Sofia museums are all at various stages of expansion programs. The Thyssen (Palacio de Villahermosa, Paseo del Prado 8, 91 420 39 44, www.museothyssen.org, closed Mon) opened its new wing in July 2004, adding considerably to its eclectic array of Western art. The giant, neo-classical Prado (Paseo del Prado, 91 330 28 00, www.museoprado.es, closed Mon) has the most ambitious – and controversial – plan, involving architect Rafael Moneo creating a cube-shaped building on the site of the cloisters of the nearby San Jerónimo church. One of Spain’s chief attractions, the Prado is best known for its extraordinary religious paintings and regal portraits by Goya, El Greco and Velázquez, as well as works by Hieronymus Bosch, Titian, Rubens and others.

The last of the trio is the Museo Nacional Centro de Arte Reina Sofía (C/Santa Isabel 52, 91 467 5062, http://museoreinasofia.mcu.es, closed Tue), Spain’s national gallery of modern art. Due to be completed any day now, the museum will gain a new façade and acres of extra space. There’s also a new exhibition space, La Casa Encendida (Ronda de Valencia 2, Lavapiés, 91 506 38 75, www.lacasaencendida.com), which hosts cutting-edge performance art and music, exhibitions and lots of activities for children.

The Habsburg dynasty dominated Madrid’s history until 1700, and the area bounded by Sol, the Plaza Mayor, the Palacio Real and San Francisco el Grande, the oldest part of the city, is commonly known as ‘Los Austrias’ after them. In fact, the Plaza Mayor is one of very few parts for which the Habsburgs can really claim credit. An elegant arcaded square with some lurid murals added in the 1990s, this was where the greatest festivals and ceremonies of imperial Madrid were held, as well as bullfights and carnivals. These days, it hosts coin and stamp collectors’ markets on Sundays and lively dance bands during fiestas. Here tourists mill around its traditional shops and pay through the nose for coffee at the cafés on its irresistible pavement terraces. Directly south of the Plaza Mayor, in C/Toledo, stand the twin baroque towers of San Isidro (No.37, 91 369 2037), a hulking, yet imposing, church. West from here, the area between Plaza de la Cebada, Mayor and the Palacio Real is the oldest part of the city, the site of the morería (the Muslim quarter) and medieval Madrid.

Tucked away in side streets in these parts are the church of San Pedro el Viejo (Costanilla de San Pedro 1, 91 365 1284), with a tower dating from the 14th century, and the 12th-century mudéjar church, San Nicolás de los Servitas (Plaza San Nicolás, 91 559 4064).

Sol is Madrid’s most photographed square, home to the emblematic bear and strawberry tree statue, as well as the famous Tío Pepe sign. The area north and east of Sol is dominated by the two great avenues of C/Alcalá and Gran Vía. C/Alcalá, once described as the grandest street in Europe, has a wonderful variety of 19th- to early 20th-century buildings, including the stunning Círculo de Bellas Artes (No.42, 91 360 5400, closed Mon), with its fine café. Look out too for the handsome Real Academia de Bellas Artes de San Fernando (No.13, 91 524 0864), with 13 works by Goya.

The stamping ground of Madrid’s Golden Age literary set remains an important theatre district today; the literary tradition lives on in cafés such as El Salón del Prado (C/del Prado 4, 91 429 3361). One survivor from the Golden Age is playwright and poet Lope de Vega’s charming old house (C/Cervantes 11, 91 429 9216, closed Mon, Sun), standing, somewhat ironically, on the street named after his enemy, Cervantes.

The author of Don Quixote himself, however, lived just around the corner on C/León, and he was buried in the convent of the Trinitarias Descalzas, which is to be found not too far away on C/Lope de Vega.

The straight grid of streets that forms the district of Salamanca was where the most affluent families built their houses and palaces in the 19th and 20th centuries. The heavy traffic doesn’t make the area very amenable for strolling, but there are places of artistic and architectural importance dotted along the Paseo de la Castellana: the Palacio de Linares, now the Casa de América (Paseo de Recoletos 2, 91 595 4800, www.casamerica.es, closed Mon), showcases Latin American arts, while the unconventional Museo de Esculturas al Aire Libre (Paseo de la Castellana 41, no phone) is an outdoor sculpture garden, providing a setting for works by Joan Miró and Eduardo Chillida. On the easternmost edge of Salamanca is Madrid’s neo-mudéjar-style temple of bullfighting, Las Ventas (C/Alcalá 237, 91 356 2200, www.las-ventas.com).

The Retiro can’t claim to be Madrid’s green lung in the way that the Casa de Campo can, but it has an ineffable charm nonetheless. It’s the place to promenade and on Sundays, particularly, there are vendors hawking everything from wafers to etchings, tarot readers, football and elderly men playing petanca. Below the Prado is the verdant Jardín Botánico (Plaza de Murillo, 91 420 3017, www.rjb.csic.es), with more than 30,000 plant species.

• Tourist information: Plaza Mayor 27, Los Austrias (91 588 1636, www.munimadrid.es); Barajas Airport (terminal 1); Chamartín station (near platform 20).