Carl,
All 3 are good courses, Royal Belfast and Belvoir were designed by Harry Colt. I am slightly biased being a member of Belvoir but it is the best of the three courses, a Harry Colt classic with a wonderful routing and 5 of the best par 3s you will find anywhere. It is only 3 miles from the centre of Belfast and yet you only see houses when coming up the 18th hole. Please let me know when you are visiting and I will try to help.
Regards,
Johnny Browne