Hi!!
Sorry just for answering now, but work has been hell!!
The best advice i can give is if you are with friends is to rent a car and drive through the countryside!!
Another alternative is doing the tours that are usually avaliable in the hostels. That way, you''ll get another perspective on history and costumes that only the local people have.
Some places: Dublin, Bend of the Boyne,Cork, Blarney Castle, Killarney, The ring of Kerry, Galway,the cliffs of Moher and the burren,Giant's causeway and Antrim coast, etc...
There is a lot to see, basically in the countryside, the cities itself aren't that interesting!! Go out to the pubs and ear some irish music (if you ear too much it will sound the same repertoire), altough it is a great experience.
If you have other questions, don't hesitate in asking!!!