A tour along the north coast would be quite spectacular. The coast road from Larne to Derry is astounding. Mad geology, beautiful landscapes that change at every turn, views to Scotland (pretty often), cliff-top castles and it's all on top of each other. Travel for five minutes and there will be something new and amazing to explore. If you take the Torr Road from Cushendun past Fair Head on a clear day - you'll have to able to crank yourself up some stupidly steep roads - but the views would be breathtaking.
White Park Bay. Displaying one of the quirks of the northern coast. There is often a strip of glorious sunshine that runs along the shore where the weather hasn't had the chance to realise that it's finally hit land. Two miles up the road and it will have been dull and drizzly all day, on the beach - uninterrupted sunshine. The fact that the gulf stream swirls round the north coast also means that the weather is generally pretty mild and is probably why many of us that had family holidays in these parts managed to survive childhood. It also explains the beach resorts and palm trees. Mind you, if there is an interesting Atlantic weather system coming in you're going to get it in the face.
Donegal from Downhill Demesne. The spectacle just keeps on going. Another micro-climate just round the corner from where this photo was taken lends a very different atmosphere to the coast road. Between the cliffs of Binevenagh and the Foyle shore they mainly grow grass. Huge expanses of lawn to be used as sporting turf. It's an odd place with the mountain looming over it and the flatness of Magilligan Point reaching out to Donegal.
Mull of Kintyre, Sanda, Aisla Craig and the Galloway mainland from Rathlin. I'd recommend Rathlin as a stopover with an easy day to follow. Cycling is the most convenient way of getting about the island even if there isn't that far that you can go. There is the RSPB reserve and upside down lighthouse at the western end of the island and lots of good walking, plus the chance to sample the unique atmosphere of Rathlin island life - they're a bit unconventional (the members of my family that live there certainly are).
One of the characteristics of the north coast that stands out is that, apart from the Giant's Causeway, it's not overrun by tourists, especially the further west you go. Maybe it's best if I don't recommend it as a destination.