There's an excellent session every sunday night from about 8:30 at the Golden Ball, a pub on a street parallel with and to the right of Micklegate (looking in to the town centre) whose name I can't remember. There's usually about 7 or 8 musicians (fiddles, squeezebox, bass, guitar, sometimes a banjo (often played by me)). The music is often American Old Time, maybe some old english fiddle tunes, various other stuff depending on who's in - not usually Irish because this gets hammered to death in other places. There's another more folky session at a pub called the Maltings on, I think, a tuesday but I've never been, although I believe its good.
The beer is excellent in both places.
Cheers
Ray