Barcelona is on of my fav places I've been.
Firstly, don't be put off by any beggars and pick pocket stories you hear. ComMOn sense will keep you safe, and it's no worse than any other city, and there's plenty of (both spanish and catalan) police about too.
You'd be hard pressed to get bored. There's LOADS to see, with Gaudi's work being the obvious place to start. We used the old faithful Lonely Planet which is worth getting a copy of.
Try and get somewhere on/near La Ramblas, which is the main street. Lined with bars, and places to eat, and with loads of small winding streets leading off from it, and some pretty good buskers. Can't remember then name of the hotel we stayed in, but it had a balcony overlooking La Ramblas and was nice to just sit there and watch the chaos below and have a drink to end the night.
It's possibly THE MOst 24hour place I've ever been, including NY.
Obvious highlights are the Gaudi stuff. The Sagrada Familia is aMOngst the MOst amazing buildings you'll ever see! The aMOut of detail is truely amazing! Be warned though, if you plan to go right up the towers, the spiral staircases can be a PITA to get up. They're only wide enough for one person, and there's people using them in both directions. There's a few windows and such you can duck into and wait for a gap to make ur way up/down in though. There's a park outside it which is ideal for taking pic's
The gaudi park is spot on too! If you've ever took acid, it'll all seem strangely familiar somehow

It's a steep treck to get there (complete with outdoor escalator), but well worth it.
You should be able to get a guidebook which will point out various other Gaudi works throughout the city. The Lonely Planet one we used was good.
The olympic village was good too. Not really much there, but it's worth seeing and the views are great.
I don't think you've mentioned being into football before? But Barcelonas stadium was a personal highlight for me. We went there hoping to get a sort of tour,, but turned out to be a matchday so we got tickets off a tout for quite cheap and wached the game

All the touts seemed to be about 80+ year old women! We ended up on the very top tier, and if you're not comfortable with heights, be warned!
Overall I found it to be the kind of place where you can just walk about and stumble across something of interest. The metro was nice, clean, simple, etc... but I always prefer to walk as much as possible.