Museo Reina Sofía

If the Prado is Madrid's past, the Reina Sofía is its twentieth century, and it holds one painting that justifies the trip on its own: Pablo Picasso's Guernica. Painted in a few weeks in 1937 after German and Italian planes bombed the Basque town of Guernica for the Nationalist side in the Spanish Civil War, the vast black, white and grey canvas — a screaming horse, a mother with a dead child, a bull, a shattered soldier, a light bulb like an eye — was shown at the Paris World Fair and then spent decades in New York, because Picasso refused to let it come to Spain until democracy returned. It arrived in 1981 and has been here since 1992. Seeing it in person, at full size, in a room with Picasso's preparatory sketches, is one of the great experiences in European art. Around it, the collection tells the story of modern art in Spain and beyond. Salvador Dalí is here with major early works, Joan Miró with luminous canvases and sculpture, and Juan Gris, María Blanchard and the Cubists with them; there are rooms on the Surrealists, on Spanish art under Franco and in exile, and on the post-war avant-garde, with international names from Francis Bacon to the Pop and Conceptual artists. The museum occupies the former General Hospital of Madrid, a severe eighteenth-century building by Francesco Sabatini, softened by two glass lift towers added on the façade, and a red-roofed extension by Jean Nouvel around a courtyard, which houses temporary exhibitions, the library and a café.

The museum is organised as a series of collection displays that are periodically rehung, so it is less a fixed list of rooms than a narrative, and the labels and wall texts are unusually thoughtful about history and politics. Guernica is on the second floor of the Sabatini building, in a room that tells the story of the Civil War and the 1937 Spanish Pavilion in Paris, where it was first shown alongside works by Miró and Alexander Calder. Give it time: stand back to take in the whole composition, then move closer to the details, and visit the room of studies beside it to see how Picasso built the image. Photography is not allowed in the Guernica rooms.

Visiting well: the Reina Sofía is closed on Tuesdays, not Mondays like many museums, which makes it a useful Monday choice. It stays open later than the Prado on most evenings, and entry is free for set hours on several evenings and on Sunday afternoons, when queues form but move quickly. Timed tickets let you skip the ticket line on busy days, and the Paseo del Arte pass covers it along with the Prado and Thyssen. The museum also runs exhibition spaces in the Retiro, at the Palacio de Velázquez and the Palacio de Cristal, which are free to visit when exhibitions are on. The ride up in the glass lifts, with views over the Atocha neighbourhood, is a small pleasure in itself.

Location makes it easy to combine: it stands opposite Atocha station, at the southern end of the Paseo del Prado, a ten-minute walk from the Prado itself. Many visitors do the Prado in the morning and the Reina Sofía in the late afternoon, ending with dinner in Lavapiés, the multicultural neighbourhood just behind the museum, or in the Barrio de las Letras up the hill. If you only have an hour, see Guernica, the Dalí and Miró rooms and the courtyard. If modern art is your passion, this is a half-day museum, and one of the most rewarding in Europe.