Ok, I lived in West London for 20 years. Variously Putney, Clapham, Fulham, Streatham, West Kensington. So here's my Londoner's view.
In terms of distance from the centre - and bearing in mind everything is on a MUCH smaller scale and distance - think:
Zone 1 - Clifton, Redland, Cotham, Stokes Croft, Montpelier
Zone 1/Zone 2 borders - Totterdown, Bedminster, Bishopston, St Andrews, Henleaze, Redcliffe, Southville, Westbury-on-Trym
Zone 3 - Brislington, Fishponds, Downend, Long Ashton
Zone 4 - Filton, Kingswood, Emersons Green, Patchway,
Overland - Clevedon, Weston Super Mare, Keynsham, Dundry, Portishead, Almondsbury
And in terms of areas, bearing in mind there are good and rubbish bits of every area, I see them as follows in terms of the vibe/feel (and I'm biased, but to a London view, so...!) if you like:
Fulham/Putney (minus the river): Clifton, Redland, Cotham, Westbury-On-Trym
Richmond: Long Ashton, Clevedon, Weston, Dundry, Almondsbury
Clapham: Bishopston, St Andrews, Redcliffe, Fishponds/Downend
Streatham: Montpelier, Totterdown, Bedminster, Henleze, Southville, Kingswood, Emersons Green, Portishead
Tooting: Stokes Croft, Brislington
Milton Keynes (vibe not location!): Filton, Patchway
Personally, I chose to live at the point where Downend/Fishponds/Staple Hill merge; its like living in a Clapham suburb: the houses and the cafes and the shops feel very familiar here, and Snuff Mills and Oldbury Court are right here. But also I'm still in London a lot and the M32/M5 is 10mins away as is Bristol Parkway station, which is 15 mins faster than Bristol Temple Meads to London. (I started in Montpelier, but I feel more at home here.)
And yes, everyone here seems to buy houses and have babies before they are 30, but don't worry, there are loads of ex-londoners here, it's the number one destination for people moving out - and with great reason.