Definitely go to the food market that is just off las rambas. There is also an excellent cocktail bar at the top of las ramblas caled Boadas. Look at the Gaudi architecture. We only looked round the outside of the Sagrada Familia though as we thought it was quite expensive to go in.
Yes yes to El Born - it's a really lovely area to wonder around in the evening. Parc Guell is good - amazing views over the city, and an interesting place to visit. The beach is nice (99% because there's people walking around selling mojitoes) but now may not be the time to go ... The Picasso Museum is excellent - lovely building, amazing collection.
In El Born there's a Tapas place called Taller de Tapas which a) is good IMO and b) also appears in "Vicki Cristina Barcelona" at one point.
I'm very jealous - Barcelona is one of my favourite cities.
You can also hire these four wheel buggy things to go driving around in, which I haven't done, but looks fun.
Oh there is the most wonderful tapas bar... I'll find the name.
Aside from that
Font du majic if its on Tourist bus Marina Wander round El Born district The food market just off La Ramblas The fairy bar for a drink (just off La Ramblas next to wax work museum) Sangrada Familiar if its your kinda thing (I wasnt impressed )