Bright pretty much has it, imo. West side of the river and up the hill a bit if you want to be able to walk into centre easily. Allt yr Yn, St Woolos, and Handpost are all pleasant and spitting distance for the centre.
I moved to the area 14 years ago, rented in Cwmbran for a while, then lived up Barrack Hill and now in Rogerstone. All good in their own way, and The current location is great for mtbing as I can follow the canal and be in Cwmcarn in 30 minutes or on the nearer hills in 10.