Giants Causeway is a little underwhelming…but the A2 up to Ballycastle is a good drive, provided its light on traffic. My favourite drive was down in Armagh; Slieve Gullion forest drive, which is 8 miles, one way, switchbacks and blind crests. Exhilarating. But you will need to check with the locals as to its condition, as in 2005, when I last drove it, it was breaking up a bit. Mournes; Spelga dam undoubtedly. as well. Windy Gap north of Dundalk. One route; pick some random roads in the Mournes, making sure you loop back Castlewellan or Tollymore forest parks, then pick up the A2 near Clough, for a really nice drive past the lighthouse. In Portaferry, get the ferry over to the other side of Strangford Lough. Aim to get dinner at Millisle.
Another drive; hit the A2 at Carrickfergus.Take a little diversion to Island Magee, to the Gobbins. Get through Larne, while admiring the Welcome signs. At Glenarfm, pull into the seafront carpark, as there is usually a bacon van there. Continue on to Cushendall, and take the signs to Cushendall. This wee little village was built in the 1920s using the English model. Its National Trust I think. Small carpark in the middle of the village, opposite the pub, but further along the road, there is a very large carpark on the left. The pub is small, but serves very good food. Continue if you dare to Torrhead. You will drive through a small village. The road can be very narrow at places, and steep awkward camber switchbacks. At Torrhead itself, there is a carpark, and then a walk up the hill to the abandoned weather station, with superb views to Scotland. Continue onto Ballycastle. DO NOT stop at the pub that meets the A2 from Torrhead; all I was told was its known to the police… Onto Ballycastle. Bit tight for parking here. I continue onto Portrush; Giants Causeway is along the way, but tis a bit busy there with tourists. Portrush is busy; popular seaside town, with a long Golden Mile. Fantastic ice cream is available. Backtrack over the Antrim Glens to Ballymena; very different from the Mournes. By Ballymena, you can join the normal commuter road to Belfast.
For motorsport enthusiasts, there is Kirkistown; we used to do little trackdays there with Trackskills. They keep the prices down, and getting on midweek is easy, given enough notice. I think his break even point was about 15 cars, @£100 each. Also, you can trace out historic road circuits. Its fun finding the Dundrod TT; the last car road race in the UK, where Mike Hawthorn still holds the lap record. Its around near the airport, and the old 50s starting grid and stands are still visible.
http://www.lfoc.org/Downloads/TracingtheTT.pdf
Another random route is the Glenelly Valley in the Sperrins.
I still have my old, tattered route map.
Oh, and the Southern tip of Ireland is a fair lick away. Dublin to Belfast; no really good roads, unless you head more to Monahagn, and get off the beaten track.