Madrid

Puerta del Sol, the broad half-moon square at the heart of the old city, is where most walks start, and the metro and the commuter trains stop beneath it. On the pavement in front of the Real Casa de Correos, the brick building with the clock tower that houses the regional government, a plaque marks Kilómetro Cero, the point from which Spain's radial national roads are measured. Nearby, a bronze bear reaches into a strawberry tree, the emblem of the city's coat of arms and a favourite meeting point. Calle de Preciados and Calle del Carmen lead north as pedestrian shopping streets toward the Gran Vía, and Calle del Arenal runs west toward the palace and the opera house.

A few minutes south-west of Sol, the Plaza Mayor is a closed rectangle of arcaded houses from the 17th century, with an equestrian statue of Philip III at its centre and the painted façade of the Casa de la Panadería on its north side. From the south-west corner, steps under the Arco de Cuchilleros drop to the Cava de San Miguel, where taverns fill old vaulted cellars. Just west of the square, the Mercado de San Miguel, an iron-and-glass market hall from the early 20th century, serves wine and tapas at its counters, and Calle Mayor continues toward the palace past the Plaza de la Villa, the square of the old town hall.

The Palacio Real stands on the bluff above the Manzanares where Madrid's old fortress, the Alcázar, stood until it burned in 1734; the palace built in its place has more than 3,400 rooms. It is the king's official residence and is used for state ceremonies, on whose days it closes to visitors, while the royal family lives at the Zarzuela Palace outside the centre. The visit climbs the grand staircase to a sequence of state rooms, among them the Throne Room under a ceiling painted by Giambattista Tiepolo, and takes in the Royal Armoury with the armour of Charles V. On the east side, the Plaza de Oriente, with clipped hedges and statues of early Spanish kings, faces the Teatro Real, the opera house, and below the west front the Campo del Moro gardens fall toward the river.

Facing the palace across the Plaza de la Armería, the Almudena Cathedral was begun in 1883 and consecrated only in 1993: a neo-Romanesque crypt below, a neo-Gothic nave above and a classical front that answers the palace. Down the Cuesta de la Vega beside it, a stretch of the ninth-century Muslim wall, the oldest remains of the city, stands in a small park. A little further south, the gardens of Las Vistillas look west over the river valley to the Casa de Campo and, on clear days, to the mountains of the Guadarrama.

La Latina, south of the Plaza Mayor, keeps the crooked streets of medieval Madrid around the Plaza de la Paja and the domed church of San Andrés. Its taverns line the curving Calle de la Cava Baja and the parallel Cava Alta, and on Sundays from midday the quarter fills as Madrileños move from bar to bar. On Sunday mornings and public holidays the Rastro, the city's flea market, spreads from the Plaza de Cascorro down the steep Ribera de Curtidores with stalls of clothes, old records, tools and bric-a-brac, while antique dealers keep the side streets. The crowd is dense by late morning, and the first hours are the easiest for browsing.

Lavapiés falls downhill from La Latina toward Atocha, a quarter where families from South Asia, North and West Africa and China have settled among older Madrileño households. Its corralas, tenement blocks whose flats open onto balconies around a shared courtyard, give the streets their character, and Calle de Lavapiés is lined with Indian and Bangladeshi restaurants. The small Plaza de Lavapiés at the bottom of the hill is the quarter's meeting point, and the Reina Sofía stands at the foot of the quarter.

East of Sol, the Barrio de las Letras, also called Huertas, slopes from the Plaza de Santa Ana down to the Paseo del Prado. Cervantes, Lope de Vega and Quevedo lived in these streets in Spain's literary Golden Age, and lines from their work are set in brass letters into the paving of Calle de las Huertas. Cervantes is buried in the convent of the Trinitarias on Calle de Lope de Vega, while the house where Lope de Vega lived stands on Calle de Cervantes. The Plaza de Santa Ana, closed by the Teatro Español at one end, is ringed with terrace bars, and the streets around it stay busy late into the night.

At the southern end of the Paseo del Prado, across from Atocha station, the Museo Reina Sofía fills an 18th-century hospital, with glass lift towers set against the old façade and an extension by Jean Nouvel under a broad red roof behind it. The collection is the art of the 20th century and after, Spanish above all. Picasso's Guernica, a vast black-and-white canvas painted in 1937, hangs in a room of its own with his studies for it in the rooms beside it, and Dalí and Miró fill the galleries around.

Halfway along the Paseo del Prado, the Museo del Prado holds the paintings gathered by the Spanish kings over centuries: Velázquez's Las Meninas and his royal portraits; Goya from the tapestry cartoons and the two Majas to the Black Paintings from the walls of his own house; Hieronymus Bosch's Garden of Earthly Delights; and El Greco, Titian and Rubens in depth. Even a long morning sees only part of it, and choosing two or three painters works better than walking it end to end. The queues are shortest at opening time. On the south side, the Real Jardín Botánico, laid out in the 18th century, has shaded paths, terraces of plants and old glasshouses.

Across the Neptune fountain from the Prado, the Museo Thyssen-Bornemisza fills the Palacio de Villahermosa with a collection gathered by one family over two generations and hung in order from the top floor down: Italian and Flemish painting of the 13th to 16th centuries, then the Dutch, the Impressionists, German Expressionism and American painting to Pop Art. North along the boulevard, the Cibeles fountain, the goddess in a chariot drawn by two lions, stands before the white Palacio de Cibeles, built as the central post office and now the city hall; Real Madrid's fans celebrate their titles at Cibeles, Atlético's at Neptune. East of Cibeles, the Puerta de Alcalá, a triumphal gate of the 1770s, stands at the corner of the Retiro.

The Parque del Retiro, laid out as the garden of a royal palace and open to the public since the 19th century, spreads east of the Prado; together with the Paseo del Prado it is inscribed as a UNESCO World Heritage landscape. At its centre is the great pond, where rowing boats circle below the colonnade and equestrian statue of the monument to Alfonso XII. South of the pond, the Palacio de Cristal, a pavilion of glass and iron from the 1880s, stands over a small lake shaded by old cypresses, and further on the Rosaleda rose garden flowers in May and June beside the Fallen Angel, a fountain crowned by a statue of Lucifer.

North of the Retiro, the Salamanca district is the 19th-century grid of broad streets laid out for Madrid's well-to-do, with apartment blocks of glazed balconies and the city's fashion houses along Calle de Serrano and Calle de José Ortega y Gasset. At its western edge, on Serrano, the Museo Arqueológico Nacional traces Spain from prehistory onward; its best-known piece is the Lady of Elche, the stone bust of an Iberian woman in a great headdress.

The Gran Vía, cut through the old centre in the early 20th century, runs from Calle de Alcalá to the Plaza de España between the city's grand commercial buildings: the domed Metrópolis building with its bronze winged Victory at the eastern end, the Telefónica tower midway, and at the Plaza del Callao the curved Carrión building, crowned by its neon sign. Its theatres stage the big musicals, and the stretch around Callao is lined with department and chain stores.

North of the Gran Vía, two quarters of narrow streets climb either side of Calle de Fuencarral. Chueca, to the east around its small square, is the centre of Madrid's gay life and the heart of the city's Pride celebrations. Malasaña, to the west, centres on the Plaza del Dos de Mayo and was the home of the movida madrileña, the music and art scene of the early 1980s; its streets keep the vintage shops and music bars, and its café terraces fill on summer evenings.

The Gran Vía ends at the Plaza de España, laid out as a garden around the monument to Cervantes, where bronze figures of Don Quixote and Sancho Panza ride below the seated writer, between two tall towers of the 1950s. A few minutes north-west, on a rise in the Parque del Oeste, stands the Templo de Debod, an Egyptian temple of the second century BC given to Spain by Egypt and rebuilt here stone by stone above a reflecting pool. The terrace beside it looks west over the river to the Casa de Campo and is a favourite place to watch the sun go down.

Down the hill from the Templo de Debod, a short walk from Príncipe Pío station, the small chapel of San Antonio de la Florida holds the frescoes Goya painted in 1798: St Anthony of Padua working a miracle in the dome, watched by a crowd of Madrileños leaning over a painted railing, and Goya himself is buried below. South along the Manzanares, Madrid Río is a riverside park laid over the M-30 ring road, which runs in tunnels beneath it, with walking and cycle paths between the 16th-century Puente de Segovia and the baroque Puente de Toledo. West of the river, the Casa de Campo, a former royal hunting estate more than ten times the size of the Retiro, has a lake, pine woods and open country.