Sacrada Familia is a must. To me it’s a church I would attend only in a psychotic nightmare. Still, it is undeniably beatiful and amazingly original.
If you like Picasso’s stuff at all, definitely go to the Picasso museum, they’ve several rooms of his versions of ‘Las Meninas’ by Valazquez, as well as a gallery of his very early drawings (detailed anatomy drawings done at at 8 or some disgustingly prodigic age). Useful for dispelling the idea that Picasso painted that way cause he couldn’t make things look ‘real’.
Walk along Las Ramblas, see the flowers and the endless street performers (doing the same tired crap they do in every city). Get some seafood, I had the best calamari I’ve ever had in Barcelona.
The olympic park is kinda cool. It was eerily empty when I went there, reminds you of how useful all those millions of dollars really are after the sixteen days are over.
Anyway, good luck. You almost can’t go wrong, Barcelona is a fun city. But do be careful after dark, you’ll not run into much serious violent crime, but there are a lot of pickpockets, and petty thieves. Especially around Las Ramblas and near centers of mass transit.