When we lived in Bath, Weston was nice, with Weston All Saints being a good school.
Oldfield Park is nice, though some of it borders onto Twerton, not as nice.
Southdown wasn't too good, Odd Down too.
Combe Down good in parts, not Foxhill.
Newbridge nice, big houses, was a good school.
Batheaston has primarily large council estate, don't know the svhool.
Larkhall seemed okay, Bathampton nice.
Can't think of the rest, sorry.
Hope that helps, we moved about 4 years ago, I really miss it at times, thoug we aren't far away. Parking can be a drag everywhere.
CAT me if you want any more details.