Investigate the metro and bus service, it's pretty easy to use.
Out of town the Monastery at Montserrat is a grown-up attraction, but it is really only worth a half day. Figueres will take a day. You'll use much of your time in the city centre - and queues for the main attractions are long and start early. Possibly tolerable this time of year, though.
Don't miss the Sagrada Fam. and the roof top visit to Casa Batlló. OK you haven't!
.T.
NB there are horror stories about pickpockets in Las Ramblas. It does happen, but don't fret about it: in a group , keepyour eyes open, bags secure (etc) - everything where you know where it is - and just be aware of lurkers and suspicious type. They go for the easy victims - I've never had any problems - just be street smart.