Welcome aboard.
Barcelona is thus far my favorite city that I've traveled to. If you look in the European forums, you'll find a lot of people's posts about it, as well as accounts of some TPunk meetups (we had one there last year after a Pamplona shindig).
Anyway, here are my touristy but recommended highlights, besides all the bars & clubs
* Parc Guell & La Sagrada Familia - there's no way you can go to Barca without going to these places designed by Gaudi
* Parc de la Ciutadella - the ornate fountains alone.. wow
* Casa Batllo - a house designed by Gaudi, but so much more than a house.. worth the €€€
* La Boqueria - excellent market, especially if you like fresh fruit & veg and jamon serrano
As for off the beaten path...
* Catch the train south to Tarragona and walk along the Roman walls surrounding the Old City. Go down to the plaza of the old city and enjoy the beauty among the ruins... Follow that up by checking out an old Roman gladiatorial arena by the sea.
* Catch a train northwest toward the Costa Brava region. You can hike between the towns of Besalu and Olot, which have old medieval castles that you probably wouldn't expect in Spain.
* Forget the popular hostels in the Raval and Barrio Gothic and opt instead for some place in the suburbs, especially if you're not partying every night. Search via TPunk's hostel links and find Home Guest House - a bit out of the way, but it's on the metro line, and the experience of staying where actual Catalunyans live/work/eat/sleep rounds out the experience a whole lot more.