Jay's apartment is in a fantastic location, especially in you're into art. Right on the block there are several excellent art galleries, several good eateries, and of course Reina Sofia is two short blocks away. Most of the major attractions, from museums to churrerias, are within walking distance. Both the subway and train station are nearby, so anything outside of a short walk can easily be achieved (I did an afternoon in Toledo).
The apartment has everything you need, from cooking supplies to a space heater and AC (being there in January the heater was appreciated). Jay has posted a list of local restaurants and cafes. The apartment is great for 1-2 people, and can even fit a third (though it'll be a bit crowded) as I think the couch is a pull-out.
I was really happy with my stay and I highly recommend Jay's place.