Las Rambla is good for a wander, look for the Market on it that sells all the sweets, St Jordi I think it's called. If you go right to the bottom the artist area is phenomenal, watching these guys do there thing is amazing.
The Sagrada familia church is worth a visit, as are the other Gaudi buildings. I didn't make it to the Park Guell but it's meant to be a good visit too.
The Hard Rock Cafe on the corner of Playa Catalunya is good for a t-shirt and the square itself is good for a break and people watching.