Newgrange - a must see for those who want to travel outside of Dublin. Situated in the Boyne Valley, Newgrange is older than the pyramids of Egypt. An ancient passage tomb, albeit re-built in part, the inner tomb has not leaked since it was built. The structure is built for the winter solstice when a ray of light enters the tomb. When partaking in the tour, you can't visit the structure without, the winter solstice is demonstrated. Entering the tomb is not for the claustrophobic, but if you don't mind small areas its worth it.
There are other sites that can be visited including the such as Knowth which are also well worth a visit. If you have time to travel around the Boyne Valley there is the site of the Battle of the Boyne as well as another anicent site the Hill of Tara - the ancient seat of the Kings of Ireland.