Your tips try the food, the theatre shows, if you speak Spanish (high level); do not miss "cercanias" (towns near Madrid to be reached by short train trips), walk it through, enjoy the Prado museum.
Madrid is a wonderful city to discover. It has excellent food, active night life, many free high level exhibitions (or at veru affordable prices), good climate and nice people. Not to forget the excellent train network. A city to enjoy.