Itinerary suggestions Northern Ireland

I'm assuming you will be hiring a car? If so, check the arrangements for hiring in Dublin and travelling into Northern Ireland (they are separate countries...) If there are issues, you may want to catch the bus from Dublin to Belfast and hire a car when you leave Belfast.

Days 1 & 2 Belfast. That gives time to see something of the city, visit Titanic Exhibition... You might also be interested in the Game of Thrones Studio Tour based at Bainbridge about 40-45 min drive SW of Belfast. (The Game of Thrones bus tours from Belfast will cover many of the sights listed for Day 5, so maybe discount them and do under your own steam and at your own pace...)

Day 3 head up the Antrim coast for the Antrim Glens. Each of them is very different and it is worth taking you time and stopping off to enjoy them along the way. If you are wanting to walk, Glenariff is possibly the best with several trails to choose from. One of the best is the waterfalls trail. Cushenden and Cushendahl are attractive small village. Spend the night at possibly Ballycastle.

Day 4 Think about a boat trip to Rathlin Island... Explore on foot - there are plenty of walking trails. Night at Ballycastle

Day 5 - Causeway coast - Carrick a Rede Rope Bridge, Dunluce Castle and Giant's Causeway. The Giant's cCauseway is always busy so try and visit first think or later in teh afternoon when all the visitors are heading back home. Also try and plan for low tide when more of the stones are exposed. At high tifde it can be a bit disappointing. As well as walking down to the stones, consider a walk along the cliffs above the causeway. You look down on the rocks and all the visitors scurrying around a bit like ants. It is an exhillarating walk. If time allows continue to Portrush and Port Stewart. Return to Ballycastle for the night.

Day 6 return to Belfast and drop off the car. Bus back to Dublin

Day 7 Fly out of Dublin (Depending on time of flight, see something of Dublin....)

If you don't want to visit Rathlin Island then look at this...

Day 4 - Causeway coast - Carrick a Rede Rope Bridge, Dunluce Castle and Giant's Causeway. The Giant's cCauseway is always busy so try and visit first think or later in teh afternoon when all the visitors are heading back home. Also try and plan for low tide when more of the stones are exposed. At high tide it can be a bit disappointing. As well as walking down to the stones, consider a walk along the cliffs above the causeway. You look down on the rocks and all the visitors scurrying around a bit like ants. It is an exhillarating walk. Drive to Derry for the night

Day 5 Explore Derry

Day 6 return to Belfast and drop off the car. Bus back to Dublin

Day 7 fly out of Dublin (Depending on time of flight, see something of Dublin....)

All good advice from Wasleys.
Some other attractions in the area that might be of interest: There's an abandoned famine village in the Glens of Antrim called Galboly, featuring the ruins of a couple of thatched cottages dating back to the famine years of the 1840's - used to be home to about 60 families.
A good place to stop for lunch is the tea room at Glenarm Castle. There are tours of the castle and there's a very pretty garden there as well.
The hike above the Giant's Causeway is indeed a pleasant one though it can be windy too. If you go far enough to the west you'll get a glimpse of the bay where one of the ships from the 1588 Spanish Armada (the La Girona) foundered. It's artifacts are on display at the Ulster Museum in Belfast. Another Armada ship sank further up the coast and it's artifacts are displayed in the Tower Museum in Derry.

Thank you, both of you!! This is just what I wanted. Appreciate your time.

Good suggestions above, a few additional thoughts from me:
-If you want to see some of the GoT sites on your own, that's pretty easy- including the Dark Hedges, Castle Ward (which you will recognise as half of the entrance to Winterfell, which was digitally doubled), and my favourite, Ballintoy Harbour which was the Iron Islands- a very beautiful location on the coast near Giant's Causeway.
-If you plan to just stay on the Antrim coast I don't have much to add beyond what's been said (except for to visit Bushmill's distillery if you are a whiskey fan)- but if you have time to explore the Down coast (south of Belfast), in addition to coastal scenery you have the Mourne Mountains, which are an excellent example of Ireland's natural beauty and great for long walks. You can visit them on a day trip from Belfast.
-In Belfast, in addition to what's been said I recommend SS Nomadic (White Star Line tender ship), St George's Market (lots of local crafts/products), and the Ulster Museum. If you want a walk in Belfast, I recommend heading up to Cave Hill where you'll have a wonderful view of the city, including the big cranes in the shipyard.
-If you have time to visit other parts of NI, one of the most beautiful areas is Enniskillen in County Fermanagh, which is on two lakes. There's also the Marble Arch caves nearby which I haven't gotten to yet tho they look very cool (you ride thru on a boat).

Northern Ireland is quite compact and you can cover a lot of places in a short time. Good luck and enjoy your trip!