Been there twice for climbing but it's been a few years.
It will be really hard to get around without a car -- both times did the short term lease thing which worked great. Don't know much about public transportation there but my guess is it's very limited.
There are tons of mind-blowing crags out of Barcelona, but require 1-2 hrs of highway and country road driving. We camped 99% of the time, which can be easy or hard depending on what time of year you're going -- in the off season, lots of the towns in the country shut down limiting food, etc.
Can't miss areas: Rodellar, Siurana, Terradets. Killer limestone. Also climbed at Monsant, Alquezar, and Montserrat. The crags are either conglomerate or limestone, all of which is better than anything we have here in the US. Pretty good info on these places if you just google.
Also have climbed down south but much preferred Catalunya/Northern Spain. Be prepared that once you get back, your radness scale will be a little skewed!
"The only reason for time is so that everything doesn't happen at once." - Buckaroo Banzai