Medialab Prado is the coolest place to work, to collaborate, to do workshops, to participate in events and conferences. They are the nicest people in the planet doing such interesting programs. My favorite is Interactivos. It is also a good place to meet new friends and go afterwards for beers in the bars around Lavapies, a district full of art galleries and Museums.
Going out in Chueca, the gay neighborhood of Madrid and grab a beer in the bars around is fun. One of my favorite programs is going to tranvestite´s concerts there.
Reina Sofia museum is always a good idea. And it's never enough of Picasso's Guernica as well as the other modern art gems. Save some hours for visiting and then look round the corner and have some wine at NuBel.
One of my favourite places to enjoy a beer bathed in orange lights and layered walls. They used to give concerts downstairs. Unfortunately they got recently banned due to boring local regulations - hopefully, live music will return soon amongst their palm trees and tropical lights.