Hi maarten!
Sorry for the delay but i've just finished working. I think the best you can do is spend friday evening-night in Sol(metro lines 1-2 and 3). There are many great pubs and discos; once there you should ask for the ones which close the latest as many of them closes at 3!(but don' worry because there are many open untill 6........but you have to look for them, jeje).
On saturday you can try with another zone called "la latina". I prefer to spend the night from bar to bar instead of staying in the same place(even if the place is a big disco)
Ihope this can help yoy, enjoy your stay!