One of the best guide is called Guia del Ocio (http://www.guiadelocio.com/madrid). Buy it on Friday to find all the information on concerts, cinemas, museums, restaurants, ...
Museums
Madrid has a lot of very good museums: the Prado, of course, but also the modern art center Reina Sofia (in front of Atocha station), the museum Thyssen (between Atocha and Cibeles)... etc. Don't forget to check Guía del ocio in order to know which day you can visit the museums for free.
El Museo del Prado : THE museum of Madrid.
El Museo Reina Sofia
El Museo Thyssen –Bornemisza: Small rooms; start with the 3rd floor to have a visit in chronoligical order.
El Palacio Real: free on Wednesday for EU citizens.
See also la catedral de la Almudena on the left of the Palacio real and the parc Campo del moro on the right.