For anyone staying in Madrid for at least three days, I would highly recommend a day trip out to Toledo. It is only about 30 minutes away by train, and is one of the most beautiful places I have seen in Europe so far (it is currently tied with Venice for the top spot). This is an old city, still maintains a medievel feel, and offers a perfect mix of Western and Muslim influences in its art, history, and architecture. We were also quite fortunate that–though much of our Madrid trip was plagued by rain–our day in Toledo was sunny and (comparatively) warm.
Warning to the elderly, infirm, or desperately out of shape: This city is on a hill, and there is a bit of a hike to get to it from where you are dropped at the train station. But it is so worth it.
So once upon a time in high school, I took two years of Spanish. Many of my classmates strongly suspected that our teacher (whose last name was so comical that it would sound fabricated if I were to share it) did not actually speak the language, though; we spent a lot of time listening to cassettes while she dug in her ear with the cap of her pen, so there was very little actual speaking. The ear digging was so gross and distracting that I learned very little, despite managing to get A’s. At university, I gained literacy in the language (though not fluency). Thus, upon moving to Europe and surrounding myself with French speakers (who I may have mentioned are not too open about sharing their language with anyone other than fellow native speakers), I had an immediate desire to put some of my language skills to the test.