The path is formally known as Graig Road, though this section isn't open to traffic.
There are numerous ways to join the path, but if you have time, I'd recommend walking the stretch between Penmaes Road & Upper Cwmbran. In between the houses and trees, there are some impressive views across Cwmbran, Newport, Wentwood, further to the Bristol Channel and beyond.
The Cistercian Way crosses Graig Road and, if you choose, you can follow it all the way to Conwy and back(!) Or you could just walk back to the car.