Yes I know Lydney, I live about 4 miles away.
Transport, it has it's own rail station and quite a few buses but none that go to Chepstow. There is a good sports centre, indoor and outdoor swimming pools, and a happy community. Not so sure about the social activities I guess that depends what you're interested in.
I would rate the area as very safe.
You say you're interested "near Bristol", though I can make Bristol centre in just over 30 minutes (traffic allowing) there is the toll to pay on the M48 Severn Bridge return journey.
Other areas, Thornbury is a similar size town with the added advantage (if you want Bristol) of being on the other side of the river. The disadvantage, it's not on the edge of the beautiful Forest of Dean ;o)
If you have any specific questions I would be happy to find you some answers, either through here or PM me.
Best wishes, G.