I live in the North, about 30 miles from Belfast. Like Dublin in the south, the best places are away from the city. Having said that I prefer Belfast to Dublin, as it’s a bit more real. No silly temple bar fake Ireland nonsense.
There are some excellent restaurants in the city, particularly if you like steak, Northern irish beef is the best within the British Isles, in my opinion. Like others have said before the museums and Game of Thrones tourism is fantastic…. If you are a fan.
if you are golfer there are many great courses, although be prepared to pay top dollar for the likes of Royal County Down or Portrush, but worth it for the experience.
if you are coming with the missus why not “Bangor for a week”… just outside Belfast 😜