If you want to get away from the main tourist spots we went to an amazing arts/music festa in an area called Gracia where they decorated all the streets in all sorts of crazy ways – not sure what it’s like normally but it seemed like there were lots of cool bars/restaurants/shops etc.
Gaudi stuff is cool just gets very busy. The Parc Guell was nice, to get out of town a little. The hills above Barcelona give a great view over the city, you can get a funicular railway up that links with the main train system.