Totally depends on her interests and whether she wants to see the leprechaun side of Ireland or a bit more of interest.
Around Cork, Blarney Castle and if it would interest her, the Midleton Distillery.
Killarney National Park, the lakes, Gap of Dunloe etc.
If she wants something more relaxing than straightforward sightseeing, going to some of the islands in Roaringwater Bay. An alternative might be a trip to the Aran Islands when you're up at the Cliffs of Moher.
Further afield, Newgrange and Tara. They can be done on the same day from Dublin. Make sure you book your Newgrange tickets in advance.
If you head up North, the Giant's Causeway. Get there by driving along the coast from Belfast, instead of using the fast inland route. One of the most underrated places in Ireland is the Fermanagh lakelands, although how interesting that would be to a foreigner, I'm unsure.
Almost forgot... The Rock of Cashel. And if you're in the area, Cahir Castle or Kilkenny Castle are worth seeing.