Here are a few nice places to visit, have a google and see what takes your fancy:
Dingle, Slea Head Drive, Inch beach,
Skelligs Islands
Clare Burren National Park,
Doolin,
Don Aonghasa on the Aran islands
Clifden and Sky Road,
Leenane,
Achill Island (there a bridge!)
Brú na Bóinne, Trim Castle
Slieve League, Glenveagh & Kylemore abbey
Donegal coast & beaches
Causway costal route (Derry to Belfast),
Belfast to Newcastle to Rostrevor
Rostrevor to Carlingford (via the short ferry)
Failing that just follow the Wild Atlantic Way!