Yes, it seems like there's a small airport in Galway (GWY). Try http://www.fly.to/galway/
According to this homepage, Aer Arran is the only airline at GWY, flying to DUB and LTN. The pictures seem a little bit outdated, Aer Lingus Saab 340, Crossair, ... I'm not sure how often this homepage is updated.
ps: If you plan to visit Galway, take warm clothes with you - I've been to Shannon in May and it was *cold*!