The Burren, get out and walk it!
Ailwee caves or if you're much more adventurous contact the adventure centre and they may be able to bring you underground into an untouched cave.
Doolin, for the music, craic and boat to Inisheer.
Cliffs of Moher
Fab beachs all over coast. Learn to surf at Lahinch.
Eat at Gregans castle, Ballinalacken castle, Byrnes in Ennistymon
Go to Galway city for a day, there's nearly always some festival on!
Loop head peninsula, total unspoilt nature and few tourists.
Ennis, nice small town, good boutiques.