I have been trying to think of things and places that you might want to go and see.
Don't know if you are sailing to Larne or Belfast but here are a few things which may or may not be of interest.
About four miles from Larne there is a place called Carnfunnock Country Park which has a nine hole golf course, crazy golf, minature railway, walled garden, mini cars and adventure playground. Not a bad wee spot especially if weather is decent. There is a wee coffee/gift shop where you can get snacks etc but in good weather some people barbeque.
Coast road has some nice views.
National Trust have some nice properties over here and some have beautiful gardens. Mount Stewart is nice and maybe
your relatives might enjoy it.
Ulster Folk & Transport Museum on Bangor Road, Holywood might be worth a visit.
In Belfast you can go on city sightseeing trips on special buses and I think there is a web site called gotobelfast.com.
If you fancy a drink you could tryhttp://www.crownbar.com/
Try looking at this http://www.visitnorthernireland.com