Lying 100 mi/160 km east of Madrid, Cuenca, Spain, is known for its hanging houses, which perch precariously on high cliffs overlooking the Huecar River. Set inside one of the hanging houses, the magnificent Spanish Abstract Art Museum displays works of Spanish abstract artists and sculptors, Gothic murals and other items (http://www.march.es/arte/cuenca). The best views of this emblematic building are from the river gorge below; the upper city in turn offers some stunning panoramas of the surrounding countryside.
All the main sights of interest are contained within the compact and picturesque old quarter, which is a delight to wander around and explore at will, The Cathedral has some splendid silver and gold work in its Tesoro Catedralicio and the Museo Diosiano houses further treasures.
The city is also a good place to shop for ceramics.
Just a few miles/kilometers outside the city is the Ciudad Encantada, a natural park whose surreal conglomeration of ancient limestone outcrops has been naturally eroded into the forms of animals such as crocodiles and elephants; some even resemble human beings. The most realistic collection of these "statues" is located in a closed-off, pay-as-you-enter zone complete with restaurants and even a hotel.