If you want to go to tintern abbey by car, then your flexibility improves. I'd suggest looking at potentially staying 1 - 2 nights in either Abergavenny or Monmouth - two small market towns with significant history and attractions, plus fine eating nearby. The whole area is full of ruins and castles, and in particular I recommend Llanthony Priory as a remote but lovely ruin (arguably far nicer than Tintern) in the depths of the Black Mountains. From there you have the Brecon Beacons (hilly moorland) close to Cardiff.
It is roughly 90 minutes drive from Bath to Abergavenny on good roads, so its a lovely trip.