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, ...
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.
See also la catedral de la Almudena on the left of the Palacio real and the parc Campo del moro on the right.