There won't be any local festivals at that time (or at least I don't remember any). If you like sports, go to a soccer game, on saturdays or sundays. If you like culture don't miss Prado, Thyssen and Reina Sofia, although they'll be crowded with tourists. If you like nightlife just walk around the old city, go to Huertas or anywhere else and you'll enjoy it. Remember not to go to a restaurant before 10pm.