Ditto on everything Lowden said. (Even the part about Paris...was just there in September!!)
I suggest seeing anything and everything Gaudi, because you won't see anything like it anywhere else. Be sure and visit the homes he designed...just all a wonder.
Fountains at night on weekends when they play the music.
Picasso museum as well and Gothic quarter.
Be prepared to dine late and they have a most serious siesta...2-3 hours and NOTHING is open...you have to go with the flow.
Enjoy!!! I am envious.