The places below would get my vote!
To the north
1) Mountains of Mourne, Co. Down
2) Giant’s Causeway, Co. Antrim
3) Fota Wildlife Park in Co. Cork is a fun day out with lots of animals.
4) Dingle in Co. Kerry & the Ring of Kerry
5) Wicklow Mountains & National Park
6) North Bull Island in North Co. Dublin for wildflowers in summer and the wading birds in winter - great for walking and for anyone interested in nature.
7) Whale-watching trip in Co. Clare. The Irish Whale & Dolphin Group organises trips and whale-watching courses but there are other boat trip operators as well.
8) The Burren, Co. Clare is well known for its rocky landscape and wildflowers.
9) Cliffs of Moher in Co. Clare.
10) Aran Islands, Co. Galway.