I am from Ireland, lived in Dublin and studied in Galway. If you want to get away from it all go to the Aran Islands which lie off the west coast. Hopefully the weather will be good, but you can never count on it. You may even catch the Galway Arts Festival while you are there.
If you are in Dublin over a weekend, you could head up to Johnny Foxes on a Sunday afternoon. It is a pub come restaurant, usually with traditional music.