The town of San Lorenzo de El Escorial, 25 mi/40 km northwest of Madrid, is home to the impressive 16th-century Royal Monastery of El Escorial, which was built as a summer retreat by ascetic Philip II.
The monastery-cum-palace, which also includes a church, library and mausoleum, can be seen in a whirlwind two-hour tour, though we'd recommend taking more time if possible. It boasts one of Europe's finest tapestry collections and houses sculptures and paintings (including portraits of Spanish royalty) by Spanish and Italian masters.
After seeing the portraits, visit the actual tombs of Spanish monarchs. All the kings of the last 500 years, from Charles V to Alfonso XIII, are buried at El Escorial.
Nearby, Valle de los Caidos (Valley of the Fallen) is a monument that supposedly honors those who died in the Spanish Civil War but actually celebrates dictator Francisco Franco (he's buried there).