Here are The Traveling Professor's recommendations for a short stay in Madrid

Hotel Preciados:  When in Madrid on my own or with a small group of travelers, we always stay at the Hotel Preciados.  Comfortable rooms, a great breakfast, bar and outdoor seating area for people watching make this hotel and excellent choice for a short trip to Madrid.  It is close to all attractions and we walked just about everywhere we went.

Hop On, Hop Off Bus:  On a short stay to just about any city, the Hop On, Hop Off bus is a pretty good idea.  It was slow going but enjoyable in traffic heavy Madrid, but a great bargain for us for two seniors at 10 euro total.

Tapas at Taberna Restaurante Los Ángeles:  Good tapas, inexpensive beverages, authentic atmosphere make this the place to go for at least one of your tapas meals while in Madrid. La Taberna Restaurante Los Ángeles does not start serving in the evening until 8 pm, but the bar is always open for snacks.

Favorite Museums:  While the Prado is deservedly regarded as one of the top museums in the world, on a short stay I prefer the Reina Sofia with one of the most powerful works of art ever created, Picasso's Guernica, on display.   Also a favorite of mine is the Museo Thyssen-Bornemisza.  It has a diversified collection of art from the likes of Duccio, Van Eyck, Carpaccio, Dürer, Caravaggio, Rubens, Sargent, Monet, Van Gogh, Gauguin, Kirchner, Mondrian, Klee, and Hopper.

Take a Walking Tour:  OgoTours runs a great walking tour to make sure you see all the great sites.  The website is a terrific resource  for travelers.