I definitely agree with Cat VH’s suggestion of the Ulster Folk Museum on the outskirts of Belfast. Old buildings from around Ulster have been reassembled here. There is a street scene with terraced houses, shops, bank, pub, school churches, small industries etc. The countryside area has reconstructed farms and buildings, complete with animals. There is also a very good transport museum just across the road..
The other museum I would recommend is the Ulster American Folk Park just outside Omagh. Many people emigrated from Ulster to America in the C18th and C19th. They were peasant farmers beholden to their landlord in Ireland, but in America they knew they would have their own land. The park is made up of the Irish section with houses and farms rebuilt here. The stories of the families have been researched and costumed interpreters talk about them and their way of life.
Next is a reconstruction of one of the emigrant ships that carried the families and possessions to America. Conditions on board were very poor with families sharing a small area often only six feet square. The voyage was dangerous and could take six to nine weeks. There was no guarantee of getting to a particular destination - it all depended on the winds...
Leaving the ship, you enter the American section. Some of the buildings have been brought from America and rebuilt here. Others have been specially built similar to those the early settlers lived in. Again the story of the emigrants has been traced and there are costumed interpreters in each of the houses. The story of individual families and their successes or failures can be traced from Ulster to America. Life was difficult tfor the settlers. Not only did they have to restart from scratch, they were also having to learn how to grow very different crops and different cooking methods etc.
Do spend some time exploring the Antrim Glens on the way to the Causeway coast. Each of them is very different . Glengarrif is my favourite and there are some very good walks here. The Waterfalls walk is definitely the best. If you only do one walk during the holiday, make it this one!
Rather than taking the main road, think about doing the detour around Torr Head from Cushendun to Ballycastle. The road is narrow and winding so is slow to drive but is definitely worth it for the views.
Don’t miss Carrick a Rede rope bridge, the ruined Dunluce Castle and Giant’s Causeway, on the way to Derry. The Causeway is best seen at low tide when more of the stones are uncovered. Also if time allows do follow the path from behind the Visitor centre. This climbs up onto the cliffs looking down on the Causeway and you can seen the visitors scurrying around like ants below.
Other places to think about are Andress House, a lovely C17th house in County Armagh. Or for something completely different visit Patterson's Spade Mill again in County Antrim which was the last working water-driven spade mill in daily use in the British Isles. There are demonstrations of spade working. This might sound a bit boring, but in fact was fascinating!