Are you driving north out of Dublin? If so, take the port tunnel to bypass the city traffic, then the motorway to the north. Have some Euro coins ready for the tolls. If you have the time, at Newry take either the coastal or a mountain route to Newcastle. If you take the mountain route make sure you find the highest road. If you go the coastal route, in Rostrevor drive up to the top of the hill in Kilbroney Forest: it's about a mile, narrow forest road with hairpins and 1 in 5 gradient and great views from the top. From Newcastle go to Strangford and take the ferry across the narrows, then the westerly route alongside the lough to Newtownards and on to Belfast. From Belfast you might as well take the main road to Larne, and then follow the coast road all the way round to the Giants Causeway and the northwest.