I would say on that budget you have a pretty good choice and could get something very nice
If you wanted luxury then at that budget you could get a 2 bed designer flat with double balconies on the waterfront in one of the posh developments ( no garden though) But you wouldn't need a car and its a pretty trendy place to live
Or personally i would go and live in Longfox Manor near Brislington which is only 10 mins or so drive into Bristol and use the tennis courts, swimming pool, and jacuzzi and gym My darling dh would be banished to the communal games room and would prop up the bar all day long and I would let the gardener look after the gardens for me at £850 a month for 2 beds i would be in Heaven
But back to the real world, Bedminster and Southville are nice areas especially North St and the Tobaco Factory area (although parking is a bitch) but plenty of local shops and you can walk into the city centre easily
Also Victoria Park near bedminster /totterdown is quite nice easy access to town /train station
Totterdown Central nice bit hippy chick ( i live there lol ) and lots of different houses /flats although the gardens can be small in some You have a lot of nice 3 -4 story old town house and its only a 10 mins easy walk to the train station at temple meads.
Stapleton, Frenchay Eastville Park & Snuff Mills are lovely areas as well plenty of open space, parks ( or there was last time i was out there with the dogs but with easy access to the M32 /M4 but sort of countryside village but not really ( iyswim)
Gloucester Rd Bishopton Horfield St Andrews are good areas as well with plenty independent shops bars restaurants There is a rather big prison in Bishopton but you wouldn't know its there unless you lived opposite it (lol)
Further out you have Emerson Green, Filton, Bradley Stoke, and Little Stoke, which all have good access to the M4/M32 and Parkway station
Then you have places like Long Ashton Portishead Failand and going further out again you have Clevedon Nailsea but thats more outside of bristol /somerset
Agree with other poster though avoid Easton, Not sure about Kingswood cant think of anything bad about it of the top of my head apart from Chaser Nightclub if its still their on the high st
St Pauls well, Its St Pauls, famous for lots of thing including the riots and the big street festival/carnival but that was a long time ago