Hi - I've lived in North Bristol for 8 years and work at UWE.
My mate lives in Greenbank and he loves it. The area traditionally has a very large immigrant population but he says that over the past year or two it's starting to get a much bigger 'aspiring middle class' sort of population. Lots of prams/coffee shops/etc.
Clifton is very twee (and it shows in the price) but can get very student-y during term (no parking/full pubs/etc.). Good if you like that sort of vibe, but they're mostly flats out that way, so you might get loud neighbours.
Redland - also v. student-y, though cheaper than Clifton.
Bediminster is the new up-and-coming location. North Street is full of great little bars/restaurants. There are a few estates around there which have, in the past, made it feel a little intimidating, but loads of my 'young, professional' mates are buying in the area.
North Bristol is your typical suburbia - mostly made up of the Stokes (Bradley Stoke, Little Stoke, Stoke Gifford). Good transport links to Bristol and further afield and you'll get a terraced house for £750 a month. Downside being that it's suburbia - I just spend a lot of time in town.
Oh, and since you're moving here, I'll try to recruit you to my softball team

Bristol has one of the largest softball leagues in the UK - newcomer link: http://www.bristolsoftball.com
[nonactive] . And I need talent!
Anyway - if you have any questions about the area, just ask me! I love Bristol and over the past five years it's character has completely changed. It's got great culture/shopping/etc. Good place to move to!
Oh, and there's a Costco in Avonmouth - so you'll be able to get all the jars of peanut butter you need!