When I was in Galway last (April) the best sessions were in Tigh Choili, The Roisin Dubh (week-ends @ about 6) also a venue for pay-in gigs, and the Crane. There are numerous other pubs that have sessions including The Quays and Seaghan O Neachtains. I'll leave it up to yourself as to whether you feel you can join in any of these sessions or not.

Most of the above sessions would be mainly tune-based traditional sessions. Mick Taylor's bar (next door to the Roisin Dubh) ocasionally have sessions which would tend to have less of a focus on trad music and more singing involved.