Shopping wise there is broadmead and the general city centre, clifton and the Mall at cribs causeway, these are the main areas really. The centre is quite large and you have the fantastic park street for all your uber-studenty coffee and clothes etc, then around the galleries and surrounding streets for H&M and the like.
The Mall is pretty good, however its all chain stores, H&M, Next, selfridges, john lewis and marks and spencers and so forth, also its a bit of a trek (they have buses to take you there from the centre i think) personally i dont like it because its gets v crowded and you can't escape from the place lol.
Broadmead is more varied, park street itself is often enough for me clothes wise.
Clifton i dont know much about, packed full of restaurants and bar type places mainly, but some nice (and expensive) shopping up there.