There are good sessions to be had in Galway City most nights of the week. Most of County Clare (where Shannon Airport is) is worth checking out for music, but particularly Ennis which has at least one session (usually far more) every night of the week. Ask the people at the session in Galway (on Good Friday ? - musn't be in a pub, cause they're all closed) and they should be able to point you in the right direction.

A copy of Irish Music magazine might be some sort of a guide, but ring the venue to check as a lot of their information is out of date. Also Tourist Office's may have some sort of information, although they're more likely to point you to stuff put on especially for tourists than the real thing.