dude check out mt. tibidabo its the tops (literally)
la rambla, catalunya square, definitely the dali museum its worth the 7 euro
and make sure to check out the stores, the fashion there is tops..
desigual clothing and camper shoes are 2 must visit shops, barcelona native stores known world round.
but be careful there are a handful of fake high end fashion stores out there.
careful not to let the locals on la rambla know you're american (they arent as friendly in barcelona as I had expected) + dont forget the main language there isn't spanish (its catalan)
these all may seem like tourist spots but trust me man they are the best things to see in that city
have fun man!
sagrada familia (amazing unfinished gaudi church)
casa mila (another gaudi structure)
park guell (BEST VIEW IN BARCELONA CAN SEE ALL THE WAY TO THE SHORE)