Carl,
Just a few suggestions:
Sligo area - Co. Sligo Golf club (Rosses Point, Harry Colt design), Strandhill Golf Club and Enniscrone. Very nice scenery (Ben Bulbin mountain) , nice little town and Drumcliff where W.B. Yeats is buried. Maybe not a whole lot to do here, but I don't know the area so well. It's a nice place to stay for a night or two.
Galway City - Galway Golf Club (Alister Mackenzie design; not a trophy course, but nice), Galway Bay golf course (Christy O'Connor design; supposed to be ok). Galway is a nice city to wander around; little shops, crafts, Claddagh area, McDonagh's Fish & Chips, traditional Irish music.
Connemara area - Connemara Golf Club (Eddie Hackett design). Clifden is the town to base yourself in. Connemara is in the Gaeltacht, so you'll hear people speaking Irish (Gaeilge). Wonderful scenery!
Clare - Lahinch Golf Club (OTM, Gibson, Mackenzie, Hawtree). Cliffs of Moher and the Burren (check up on this as it's an amazing landscape unique to Co. Clare). The home of traditional Irish music.
Dónal.