2 Best Sights in Castile–Leon and Castile–La Mancha, Spain

As if Cuenca's famous Casas Colgadas, suspended impossibly over the cliffs below, were not eye-popping enough, they also house one of Spain's finest museums, the Museo de Arte Abstracto Español (Museum of Spanish Abstract Art)—not to be confused with the adjacent Museo Municipal de Arte Moderno (Municipal Museum of Modern Art). Projecting over the town's eastern precipice, these houses originally formed a 15th-century palace, which later served as a town hall before falling into disrepair in the 19th century. In 1927 the cantilevered balconies were rebuilt, and in 1966 the painter Fernando Zóbel created the world's first museum devoted exclusively to abstract art. The works he gathered—by such renowned names as Carlos Saura, Eduardo Chillida, Lucio Muñoz, and Antoni Tàpies—are primarily by exiled Spanish artists who grew up under Franco's regime. The museum has free smartphone audio guides that can be downloaded from the website.

Across the Plaza del Rey San Fernando from the cathedral, this is the city's main gate, rebuilt in the 16th century by King Carlos V. Walk through toward the river and look above the arch at the 16th-century statues of the first Castilian judges, El Cid, King Carlos I, and Spain's patron saint, James.