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.