I went to Madrid for 3 days a month ago and I can't wait to go back!
There are lots of attractions but it really helps if you like art. The Museo del Prado is unmissable, The Museo Nacional Centro de Art Reina Sofia (modern art) is stunning, if somewhat confusing at times! But my absolute favourite has to be the Museo Sorolla:
http://museosorolla.mcu.es/
There's great food available (at surprisingly low prices) everywhere and getting around couldn't be easier. (The Metro system is modern, efficient and, importantly, fully air-conditioned).
Best of all though, my hotel was absolutely wonderful. It was a little 6 room pensión with an incredibly friendly and helpful manager, just 100m off the Gran Via, with TV, air-conditioning and free wifi. It was spotlessly clean and (because it was up on the 4th floor) nice and quiet. All for just €22 per night!