I dno't know of anything on Anglesey but maybe there is still something happening in Beaumaris either in the Buckley Arms or the Bull. The folk club used to move between the 2 venues. I know John who ran it had packed in but something in the back of my mind says he was interested in starting again.I am out of touch but off the Island, Bangor is the nearest venue. To the best of my knowledge, the Friday night Irish session is in the Nelson and I think that the Tap and Spile still has a Monday night Welsh session.
Other than that, the nearest venues I can think of would be the Mount in Llanwnda on a Thursday (assuming it is still going) and the Conwy Folk club on a Monday.
Jon