The thing about the Cashen course in Ballybunion is that you might just love it. Then again, you might hate it. It really does divide people.
Driving around the Ring of Kerry is absolutely beautiful, but slow. You will be on the Ring on your travels.
Dooks is worth a visit.
Jason - Killarney, Kenmare, Kinsale are good places for non-golfers to visit too. Lahinch is good fun at night, and the non-golfers can go and explore the Burren during the day. Gus Connors is a famous music pub in Doolin, which is nearby. It's worth a visit. You could also take a boat of plane out to the Arran Islands...
A good time to visit Co Clare is during the Willie Clancy festival, which is early July. Lots and lots of live Irish music in Milltownmalbay.
There's Puc Fair in Kilorglin, Co Kerry, too, where they crown a goat king every year.
Cork hosts the national Jazz festival every year on the October bank holiday weekend...
You might also get some ideas at
http://www.ireland.travel.ie/