These are all excellent suggestions I think! Though I really wasn’t all that impressed by the Prado – Sorry! All I can add is to ask around for the best chocolat y churro shop nearby wherever you’re staying (p.s. they taste better after midnight.) Maybe as a stopover between a night at a club or pubcrawl? If you’re looking for clubs, there’re a ton of great ones, but just be aware that Madrid has some strict club dresscodes, especially for men, so no shorts/open toed shoes, ect. if you’re bringing a guy friend.

Even just wandering around Madrid aimilessly is lots of fun, and though I’ve heard lots of real horror stories about crime around the city, I and a couple other girls I was hosteling with missed the last metro ride of the night and walked for 3 hours in some pretty sketch areas around 2am and were fine.
Have fun!!

Oh, and p.s. Nice Threadless shirt!