People living in Madrid love partying! The last metro is at 1.30am, but a lot of buhús (autobuses de noche) run until the morning (departure from Plaza de Cibeles, then Sol, Opera etc).
In Madrid, cinema lovers will find a large choice with plenty of movies in English or Spanish. It is cheap, really cheap. La Filmoteca (metro Anton Martin) offers a lot of films for a bargain. To find a selection of non Holywood movies: cinema Renoir and Alphaville (metro Plaza de España). Go also near Gran vía and Plaza de Callao.
To find the « Erasmus » ambiance, go to Palacio Gaviria (a former palace converted into a night club and where they organize special parties for foreign students every Thursday), calle Arenal. There is also the Kapital, with 7 floors, close to Atocha. Generally, do not go to a night club before midnight, you won't see anybody...