Cheltenham is probably the best area in the county. Good areas within this are Leckhampton, Charlton Kings, Prestbury....... Montpellier and Bath Road are nice shopping areas as well as the town centre. It does have a fairly large affluent feel but there are equally some very deprived areas. Schools are very good, however.
Stroud has more of a "hippy" vibe, and is a bit tired/poor in the town centre but nice areas around it are Chalford, Bisley, Minchinhampton, Nailsworth but it's all a bit more rural and with teenagers, you're going to spend hours in the car to Cheltenham and back!
Gloucester has good schools as mentioned previously but is an absolute dump of a city centre and Mecca for the £shopper. There are a few OK restaurants and hairdressers but we avoid it like the plague even though it's closest. The Forest of Dean is equally deprived and run down, albeit picturesque. Best avoided.
Someone mentioned the areas between Gloucester and Tewkesbury - best avoided unless you like long journeys when the Severn floods. And it does at least 3 or 4 times a year.
If we didn't have family ties in this area, we'd move up to the Cotswold area. I like the outlying area around Cirencester - lots of quintessential cotswold stone homes but sadly not a lot of house for the money! Compton Abdale is my current favourite, or Withington, Hampnett, Hazleton. Lovely villages and not far from Cheltenham or Cirencester.