I have had a couple of visits to Northern Ireland, flying both times from Birmingham to Derry. On my first visit I toured around some of the beautiful countryside and mountains around County Tyrone and ventured into the south (Eire), County Donegal, which is actually to the west of Derry. Apparently if you can see Donegal from across the Foyle then rain is on its way, if you can't see it then it is already raining. There is a reason why it is known as the Emerald Isle!
On my second visit I went to the Rope Bridge (Carrick-a-Rede) and the Giant's Causeway on the northern coast. Despite being cold and windy, we had sunshine and blue skies most of the time which showed off the glorious coastline.
There is definitely lots to see here, even if the weather can't be guaranteed you will be sure to see some great sights.