Graig Road runs from Greenmeadow to Upper Cwmbran. The views over the town are great. If you are feeling a bit more energetic you can bear off and head towards Mynydd Maen.
There are several info boards along the route. It takes about 20 minutes to go from the start by Penmaes Road and end up with a beer in the Bush Inn. The photos show the inside of this nice dog-friendly pub.