Bath is beautiful, but as @Churchview said, it is busy, expensive and traffic is really bad. There is a Clean Air Zone in place and a 'ring of steel' being built around the centre to exclude vehicles. Most areas around the centre are now 20mph zones and the main routes almost always very busy.
Despite this, it really is a lovely place to live. Stunning, historic, city benefits with direct access to gorgeous countryside too. There are some cheaper areas, such as Twerton/Southdown, but they are cheaper for a reason... Oldfield Park is good for families but there are also lots of students and parking is restricted. Larkhall and Weston (on opposite outskirts of Bath) retain a village-y feel so can be a bit cliquey but they are mostly calm, suburban spaces with access to local shops and good schools.
I've lived here for about 12 years now, used to live in a town about 10 miles away. If you don't need to be IN Bath itself, then Corsham, Keynsham, Chippenham, Saltford, Midsomer Norton are all relatively close (approx 30 min drive max) and would be a bit cheaper to buy.
I rarely choose to go into Bath for shopping, unless it's very early in the day to avoid parking difficulties and too many people. There are Park and Rides but the queues for the buses going back are always miles long. Plenty of places are walkable, though lots of hills so you need good calves :)
The Royal United Hospital is good. Local GPs can be a bit hit and miss, and it can be hard to get an emergency appointment.
I think the advice to rent a place and live like a resident for a week is a very good one! Where are you coming from? That can have a big impact on how you see the place. I had a friend who moved from Blackpool to Bath and she just couldn't get over how beautiful and green it is.