SO MANY MILES TO WANDER
Very close to Madrid, about 170 kms, there is a UNESCO World Heritage site called Cuenca, more specifically the Historic Walled Town of Cuenca. It was built by the Moors and the site is much known for the Casas Colgadas (in English Hanging Houses). These houses are suspended from sheer cliffs and overlooking the Huécar River.
The historical centre is not very big; however keep in mind that has many steep streets and alleys, so you will get tired. If you are looking for culture or history, check museums or churches, if you are in the mood to do some trekking, there are also plenty of choices in the surroundings.
Probably the most known museum is Museo de Arte Abstracto Español, not only you will see works of art but the building itself is a museum since it is one of the three Casas Colgadas that still exists. They consist of a popular architecture with a gothic style, and with an interior where wooden components abound. Another museum that I found interesting was Fundación Antonio Pérez, where you can get lost over the four floors of the San Clement convent, between abstract paintings and sculptures.
The Cathedral is also an interesting site of Gothic architecture, the first example of this kind of architecture in Spain, however with Renaissance and Baroque elements. You can also visit Nuestra Señora de las Angustias Shrine, on the way down to Júcar River.
Regarding walks, since the historical centre is at about 1000 meters above sea level, you have trails that descend into the deep gorges of the rivers, Júcar and Huécar. There are many choices of trails, some easier than others; for an easy one you can walk beside Júcar or Huécar rivers, or others that take more effort: the San Julian trail or up to Cerro del Socorro.
For a view of the Casas Colgadas, you can cross San Pablo Bridge, however I really enjoyed heading up to the castle, crossing the Bezudo Arc, follow the trail and seat at a rock facing Casas Colgadas and the cliff on the Huécar River side.
You can also visit the surroundings such as the Roman ruins of Segóbriga, close to Saelices; Uclés Monastery or some castles (you can check more guided tours here, but the page is in Spanish: http://hostaltabanqueta.com/excursionescuencaguia.html).
It’s quite easy to get to Cuenca from Madrid, if you arrive by plane just take Cercanías to the train station Puerta de Atocha and then take the fast train AVE to Cuenca, it will take you less than an hour with AVE train. Take in mind that Cercanías ticket is included when you buy the AVE ticket, however you will have to go to a Renfe ticket office, show them the code and they will give you a ticket for Cercanías.
I really enjoyed Cuenca, where I was surrounded by cliffs, rivers and friendly people; of course as I speak Spanish it becomes easier to make conversation with the locals. Try to learn a few words before you go.