It's great to hear you and your boyfriend are wanting to explore the Causeway Coastal Route and eight days is a good amount of time to spend doing it.
The Causeway Coastal Route going north out of Belfast is predominantly a driving route and large parts of the A2 road do not have a footpath and it is quite narrow in places. July is a busy month for visitors, so there also could be quite a lot of traffic. On the plus side, there are good portions of the route can be done off road especially the section between Ballintoy and Portstewart.
You might consider visiting The Gobbins Cliff Path at Island Magee. https://thegobbinscliffpath.com/
The Glens of Antrim provide great walking terrain and are famous for the beauty of the unspoilt, undulating landscape. Ronan's Way in the Glens is also a popular walk. These walks and many more can be found at: https://www.walkni.com
Around the Ballycastle area you have Knocklayde hill to climb. Rathlin Island is only 25 minutes by boat from Ballycastle Harbour and it is the perfect place for a day's hike. It is advisable to book the boat in advance. Torr Head with its spectacular cliffs and peaceful Murlough Bay have walking trails that are both remote and inspiring.
The 48 km off-road walking route from Carrick-A-Rede Rope Bridge in the east to Portstewart Strand in the west is a superb walk. It takes you along golden beaches and sea cliffs, through the Giant's Causeway, a UNESCO World Heritage Site and on to Dunluce Castle. Should you wish to make a short detour into Bushmills you can take a tour of the world's oldest licensed whiskey distillery. The route will pass through the town of Portrush and from there you can take the Port Path to Portstewart. There are plenty of places along the way to get a meal or to have a drink in a local pub. To find out more about the Causeway Coast and Glens region, please take a look at our web site: https://www.visitcausewaycoastandglens.com
Should you decide to use public transport for part of your journey there are a couple of buses that go along part of the route. The 252 bus goes from Larne to Ballycastle. The 402/172 Causeway Rambler bus goes from Ballycastle to Portstewart. Timetables for these buses can be found on: https://www.translink.co.uk
It is advisable to have accommodation booked in advance as the area is busy during July, however I know it can be hard to know exactly where you might be from night to night. If you require any help, please get in touch again.
Good luck with all your preparation and I wish you both an epic trip!