I fear that you may have missed the best of what the GAA has to offer as it really is pretty much in a closed season.
The main County competitions (best of the best players) are over but some club competitions are still going.
There maybe the possibility for an Connacht All-Ireland Senior Club Championship Semi-final on the 4th but who or when that will be played is very tentative so you'll have to wait closer to the time.
A small village to stay in that I would recommend is a place called Kinvara. Has 5 or 6 pubs and 1 hotel but I would imagine plenty B&B's, one pub called Greens has a fairly decent whiskey range but an even better display of whiskey as they collect a lot of different (full) bottles just for show. Kinvara is a small village with it's own Quay and a castle near by and quite picturesque. Not a far drive from Galway city and it would be maybe an hour from the Cliffs of Moher. But a lovely place of interest on it's door step is the Burren. Which is basically a unique wild rocky (nearly lunar) landscape and a unique ecosystem. You don't need to be into rare plants to enjoy this place though, great for walks and scenery and it has it's own portal Tomb and a few other bits and bobs in there. Google it I'm sure you'll learn more than I
.
The other alternative is North of Galway where the famous Connemara lies, a wild boggy land scape but I don't know enough to suggest a village.
Galway city is a great spot but will not offer you the real relaxed atmosphere that possibly your looking for. This city is always buzzing but now has some great whiskey pubs. Possibly woth making as your base though as you can do both the Burren and Connemara then
On you way from Galway to Dublin be sure not to pass by Kilbeggan. Even if people in your party are not into Whiskey the tour of the 19th Century distillery is very interesting from any historical point of view. Just check to see if it is open that time of year?!??!?!?!?
Any questions just pop them in here and we'll try to sort you out.