In reply to Tomadevil:
The demand for climbing in Bristol is massive and as such there are a lot of gyms; 3 dedicated bouldering centres (Flashpoint, Bloc, TCA) and 2 roped centres (Redpoint and UCR). They're all pretty good, though it might be a pain to get to the ones south of the river (Redpoint/Flashpoint) on an eve.
If you're leading VS, there are a few decent multi-pitches in the gorge but the better climbing starts at HVS/E1 (especially so on the Suspension Bridge Buttress). If you're leading <VS then I'm afraid the options are a lot more limited in terms of decent climbs. There is a bit of sport in the New Quarry and Quarry 3 on the other side but you'd be better off sticking to the Wye Valley for that kind of thing (the nicest thing I can say about the sport in the gorge is that it is an acquired taste). Lots of good stuff in the Wye Valley in the VS-E2 range.
Traffic on the M5 between Glos & Bristol during the busy times can be pretty horrible, so bear that in mind if you'll be commuting.