One of the favorite things to do is take a "walking tour" of Madrid. Since the central city is fairly compact, one can cover lots of sights in a short two hour stroll around the center. Tours range from walks focusing on museums in the day to ones at night that visit different types of restruants, wine bars and night clubs.

Since the night doies not really start in Madrid until 2200 (10:00PM) or so, a tour that runs from 2000 (8:00PM) to 2200 (10:00PM) gives you a great intro to many places by a knowledgable guide and then you can retire to the hotel or pick one you visited earlier or even venture to other locations for an adventure.