Top tips:
Try to get night kayaking to check out the bioluminescence – magical
Ring of Kerry or West Cork Costal route is a great day’s drive
Took the trip to Skellig Michael a few years ago – well worth it
Plenty of good beaches, mountain walks, cliffs, castles, etc.
Check out sites like groupon, pigsback, etc for discounted accommodation.
Depending how long you had I would travel about to check out West Cork, ring of Kerry, Skelligs Islands, then head North to visit the Burren, Doolin, Galway City, Don Aonghasa on the Aran island, Leenane, Kylemore abbey, Achill Island, Slieve League and Glenveagh.