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If you're spending more than a few days in Madrid, consider one or more excursions to nearby cities and monuments. Most are easy to reach by train, bus, car, or organized tour.
Toledo (see photo above) is only 50 km or 31 miles from Madrid. The city was Spain's capital for five centuries (spread over two millennia) and is packed with Christian, Jewish, and Moorish monuments. Don't miss the Cathedral (one of the world's largest) and the Alcazar, a hilltop fortress that was restored after enduring a 70-day siege in the Spanish Civil War. For more information, including transportation tips, visit the city government's bilingual ToledoWeb and Spain Tourism's Province of Toledo pages. (Tip: Although you can see Toledo's most popular sites in a few hours, you'll get more out of your visit if you stay a night or two.)
Segovia is a bit farther away (88 km, 55 miles) but is easy enough to reach by bus, train, or car. The city is surrounded by mountains, and it's famous for its Roman aqueduct, Gothic cathedral, medieval old town, and traditional Castilian cuisine. (Try to come during the week, since Madrilenos flock to Segovia on weekends.) The official Segovia Turismo site is available only in Spanish, but you'll find an English-language Segovia section at Spain Tourism's Web site.
El Escorial, the palace and monastery built by Philip II, is only 40 km (25 miles) from Madrid. The vast 16th Century building occupies a dramatic site site near the mountains, and it's well worth a visit even if royal palaces normally leave you cold. (Philip II's private apartments, and especially his bedroom, are surprisingly austere.)
Nearby, the Valle de los Caidos (Valley of the Fallen) is a monument to victims of the Spanish Civil War. It includes a basilica that was hewn out of the rock by prisoners of General Franco's winning side. Some 40,000 dead soldiers (both Nationalists and Republicans) are hidden behind the mausoleum's walls.
The royal palace and hunting lodge of El Pardo, where General Franco lived, is still used to entertain visiting VIPs, while the royal summer palace of Aranjuez (inset photo) was a hunting lodge in earlier times. The latter's riverside gardens are lovely in nice weather, and the neighboring town of Chinchon scores high on the "picturesque" scale.
For more information on El Escorial, Valle de las Caidos, El Pardo, and Aranjuez, see the relevant sections of Spain's national heritage site, Patrimonionacional.es.
Tip: Entrance to El Escorial, Valle de las Caidos, El Pardo, Aranjuez, and several other attractions outside Madrid is free to holders of the Madrid Card and Madrid Card Cultura.
Other cities: Describing every possible excursion from Madrid is beyond the scope of this guide, but there are plenty of locations to choose from--including such UNESCO World Heritage Sites as Avila, Salamanca, and Cuenca, all of which are close enough to Madrid for an overnight visit or (if you insist) a day trip. For more excursion ideas, browse the "Where to Go" section of Spain Tourism's Spain.info.