Let's see now;
Anything in the Swansea valley- OFD, Dan-Yr-Ogof, Pwll Dfyn, Tunnel and Pant Mawr Pot to name but a few.
Llethrid Swallet on the Gower-well worth a trip.
All the caves around Ystradfellte are probably within an hour of Swansea, so Porth-Yr-Ogof is a must. Dinas silica mines as well.