Used to live in Belfast, as mentioned, the Mournes is ace for riding, particularly Rostrevor, Bigwood and Donard Forest. Rostrevor is an excellent trail centre, and there’s plenty of off piste stuff to go at that’s a bit more engaging.
In terms of a general holiday, the North Coast is beautiful – will get busier depending on the time of year, and the weather can be a bit hit and miss, Donegal over in the ROI is stunning, all the way up the North West coast. Super rural and isolated, and a lot of the roads away from the main trunk roads are little more than gravel tracks. That said, pristine beaches which you’ll generally have to yourself when the weather is good is unbeatable.
One thing to note, if you were planning a summer holiday, I wouldn’t head over in July. Can get a bit lively, and a significant proportion of the population choose July to go on holiday.