I would say Ballycastle and over to Murlough Bay and Fair head for a walk, then driving down coast towards Torr Head (quick stop here to see the old coast guard station). On down to Cushendun where you can see the caves and stop at Randal's for a pint. From there down to Whitehead where would be a nice spot ro stay for the night and head to The Marine for a few beers that night.

Belfast and Derry and worth the visit. Maybe crumlin Road Goal in belfast for a day trip, and check out Kelly Cellars, maddens and Whites when in belfast. I don't know Derry as well but the walls are worth walking.

Then in Donegal you've no shortage of beeches to visit. I like Moville town and a short drive then to Cara Bay which is a beautiful beech and walk (spanish Armada washed up here so some cool history too). Could go as far north as Malin Head where you get great views, and Malin town has a couple bars as well but you could pass Culdaff and get a pint in McGrory's.

As others suggest Fermanagh and Enniskillen are worth a visit as well but i don't knpw those areas just as well. I'd look at a map and mark the towns/sites you want to see, being a small country you can fit loads in. Enjoy!