We will finish our RS 14 Ireland trip in Belfast. I have added extra days to Dublin on arrival and to Belfast at the end. I am finding limited sights in Belfast for 3+ days. I was looking forward to a black cab tour but feel it might be redundant as RS will give us a walking tour and the a bus tour on "the Troubles". New thought - might it be worth while to rent a car and drive leisurely back to the Dublin airport for our flight home., perhaps staying overnight once or twice? Any thoughts or recommendations?
I would imagine that there would be quite a large drop-off fee for renting in Northern Ireland and dropping off in the Republic of Ireland, a different country. Alternatively, you could take an Aircoach bus from Belfast to the Dublin Airport, rent a car there, and go exploring. Or, rent in Belfast, go exploring, then take the bus to Dublin.
Per Insbig, renting a car in Belfast and returning in Dublin will result in a one-way international drop charge of over USD $200. Better to rent the car in Belfast and explore a little more of the north, then return it there and catch the bus or train back into Dublin.
A meandering drive north from Belfast along the Antrim Coast would be one suggestion - it's beautiful, and you might even throw in a night or two in a castle along the way.
The Irish-American Folk Park near Omagh is also worth a stop, especially if your heritage traces to Ulster.
I'm on that tour next spring, and as I planned extra days I had the same reaction to Belfast, seems like the tour will cover most of what I want to see there. So I'll be flying home the day the tour ends, or the next day, probably from Dublin. If you've booked your flights, then I'd agree with others about the extra time -- take the bus to DUB and rent a car for some exploring on your own. Bru na Boinne looks like a first-rate destination for a day north of Dublin, should be easy to reach from the airport. I'm planning to go there before the tour.
Or you could ask people for recommendations about Belfast and its surroundings, indicating your interests and what you'll have already done. You could split your days between both Irelands, renting a car in either or both but using the bus to get between them.