Nothing at Penmon. The water for the well probably just percolates into some fields and comes out along a shale horizon. The interesting area is Fedw Fawr, where there is an active (periodically) sink - Fedw Fawr Pot. This is about 15foot deep to rubble and some fluting. Unfortunately the resurgence is only a 100m or so away at the beach. I visited years ago, and in a return visit 5 years ago, it didn't look quite the same - some how smaller. Cris Ebbs in a separate visit confirmed there are in fact two Fedw Fawr Pots! You can see the water channels on Lidar.
The only bit of limestone that actually looks 'cavernous' is at Castell Mawr Quarry near Benllech where quarrying has left the remains of a mud filled phreatic passage, and a couple of flow deposits on the wall of the large block of limestone left over by quarrying.
There is some limestone by the Straits and I beleive that some karst features were discovered when Plan Newydd was putting in heat pump equipment a few years ago.
There is a large tract of limestone in central Anglesey, dipping gently to the south. I've always fancied there may be something to be found along the escarpment facing Mynydd Bodafon - particularly where a sizable valley maybe has cut backwards into some down dip channels. Access is a bit tricky in this area though.
The owner of Stone Science mentioned 'an active passage' somewhere on the island, but for some reason he would not divulge where.
Gus Horsey also mentioned a sink and possible passage on the coast between Moefre and the Royal Charter shipwreck monument.