Retiro Park is nice place to walk, the station adjacent (Atcoha) is also worth having a look in for it's botanical gardens, lots of art gallerias nearby if that is your thing. The Bernabeu tour is great and if a game is on at Rayo (Vallecas) it is worth seeing for their crackpot fans, easily got to on the metro.
There are too many great bars and eateries to mention, you will find them, don't give up on the nightlife which really does go on till dawn and might not get started in some areas till after midnight.