Carlisle has a course under the climb out from R25. Always been curious how the locals play golf with their 13 fingers.
Alternatively, Woodvale has a certain championship course nearby, although I suspect you would be welcome at neither. They're sort of friendly like that.
How about Prestwick? Championship standard courses galore within spitting distance, and plenty more besides. If I remember right, Troon alone has 3 different courses.