Plenty of scenery up on the north coast. Ballycastle has a lovely beach and from there it's a short drive to the likes of Portstewart and Portrush, the Giant's Causeway, Mussenden Temple, Dunluce castle ruins, Carrick-a-rede rope bridge in Ballintoy etc. Morton's chip shop in Ballycastle is award-winning. It's not too long a drive to Derry - worth seeing the walls and the Peace Bridge over the Foyle river and the Derry Girls mural.
It's definitely worth taking a trip to Belfast, and beyond that there's Bangor in Co Down. From there you could see the likes of Annalong, Portaferry, Downpatrick, Kilkeel, or Newcastle where as in the song, "the mountains of Mourne sweep down to the sea"! When you are heading back to Ballycastle, make sure and drive the scenic coastal, stopping off at little villages like Cushendall, Cushendun, Carnlough. You could also stop off at the Glens of Antrim for more beautiful scenery.
For RoI, I love Co Clare, Galway city and Cork but they're probably too long a drive this time. Carlingford is beautiful if you want a sojourn over the border, and that's not too far from Newry/Warrenpoint.
Enjoy!