City centre opportunities are very well documented (Sagrada, Gaudi architecture, etc) and most are worth a visit. Out of the centre Park Güell is good on a good day, full of school kids (and other tourists) on a 'bad' one.
You can get to the Gaudi Museum at Figueres by train (or car) and it is very good for indoor shots with the right gear.
The monastery at Montserrat is a good 30mile car drive out of town - impressive, if a little 'religious' ..... There is a metro service too.
There is/was a son et lumiere at the Plaça de Catalunya at times (possibly Tuesday nights ?????) when the fountains are lit - you'd need to check this out as it's not a daily event AFAIK.