You could do a lot worse than visit the festival below. Great setting right next to Tintern Abbey, great crowd, food, beer. And plenty of opportunity to have an impromptu session and pick up some Welsh songs/tunes.
And whilst you are in the area you could do a lot worse than Rumney Folk Club in Cardiff (Third Friday). If you do go to Cardiff the Welsh Folk Museum (St Fagans) is a must. Lots of old restored and relocated buildings, smithy, clog maker, and a good section of traditional Welsh instruments and bits and pieces from past Eisteddfods etc.
Have a great time wherever you decide/end up!