Mynydd Maen and Mynydd Twyn Glas are the mountains I guess you refer to above Cwmbran? There are fire roads up through the woods and then sheep trails along the tops. There are cheeky runs through the woods.
Big Pit is worth a trip, free entry as it’s a Welsh Museum, there’s also the Rhymney brewery 1/4 mile down the road from it. Not sure if it’s open Sundays. The baths at Caerleon are impressive to look around. The amphitheatre too. You can park by the amphitheatre and walk to the baths through the old barracks. Caerleon has a one-way system and the amphitheatre is before the baths.
The food at The Lion in Blaenavon is quite nice, and if you get to Cwmbran then I can recommend the cafe at Llantarnam Grange arts centre. Park for 2 hours at Morrisons and walk across the road.