Bristol is big and bustling. Traffic is awful and house prices are high but you do get the urban feel of a city along with all the good culture/food etc. It's very cosmopolitan and I know lots of people very happy there.
Gloucester is OK. Has some good areas. City centre on the up but as a whole the place is quite run down. Those living in the nicer parts will generally travel a bit further afield to places like bristol/Cheltenham for culture etc. It's good value for money and schools are OK. Grammar area if that's relevant.
Stroud, again is mixed. It's really quite alternative though, in my opinion. Quite a happy vibe. On the flip side, it's also quite posh as lots of monied people live in the surrounding countryside. But the town itself is a little run down and not that well to do.
Cheltenham is not as fancy as it makes out, but is a good go between instead of Gloucester and Bristol. Smaller and less urban than Bristol, but still with a bit of culture and some decent places to eat. It's wealthier than Gloucester (read, posher) but it still has rough parts and is much more expensive, though cheaper than Bristol. Schools are generally good but can be over subscribed. Grammar area again.
If you fancy rural living, there are lots of really nice smaller places, but if you want a town, that's about your lot.
You could also consider Bath, it's not that far from Bristol or Gloucester.
You say you want to meet other mum's and need busses. If you don't drive, avoid Stroud. Lots of people will live outside the town and public transport is poor. Bristol will easily have the best, then possibly Gloucester.
We relocated from London to Cheltenham a few years ago, and we love it. We are very happy. More than happy to help over PM if you'd like to.
However I wish I knew now what I knew then. We ruled our Gloucester entirely, but now I live nearby I can see why people like living there!