In Cardiff Bay on Wed 12 at the Wales Millennium Centre. It's not a session, but there's a free concert at 6.15 on the Glanfa (foyer) stage with Blanche Rowen & Mike Gulston.

Llantrisant Folk Club is the same evening - CF72 9DQ. We have a singers' night so you'd be most welcome.

There are two folk clubs in Newport on Thursday night.
Newport Folk Club
Lyceum Folk Club

If you want to stay in Cardiff, Buzz magazine as comprehensive listings of city venues. One I can think off is called Gwdihw, but I don't know what nights it operates.

Have fun.

Splott Man