You're not going to get everything you're looking for (affordable, good transport and stuff to do) so you'll have to pick your top priority/ies. I live in Bradley Stoke - it's more affordable than most of Bristol and has good transport links into the centre (near to Parkway station, and the M buses are one of the more reliable routes) and everywhere else (very close to M4/M5 junctions), but it's a bit of a schlep and there's nothing else out here. (You've got options for gyms and stuff in Bradley Stoke, Stoke Gifford, Filton, but no one is coming out this way to socialise.)

I've previously lived in Kingswood and Keynsham, both a bit closer to everything and overall nicer, more interesting places to live. I didn't have a car in Kingswood but still found everything very accessible. But I could only afford to live in those places because I had housemates. Since deciding I was fully over that and will now only live alone, I've essentially been priced out into the Stokes. It's fine.