The Wicklow Mountains has two blockbuster sights, Gardens of Powerscourt and Glendalough. See also the Glenmacnass waterfall, Blessington lakes, Sally Gaps, etc. on your visit to this beautiful county.
County Clare overlooks the Atlantic and the Cliffs of Moher. The Burren is a limestone moonscape you do not want to miss. While you are in the county, make also a trip to Doolin, which was once the town for Irish and European music lovers.
County Mayo was badly affected during the Great Famine due to its remote location. Visit the National Famine Memorial to learn more. While you are in the county, see also Westport, Village of Cong, Achill Island, etc.