You need at least a comma after "golf." I think one sentence is okay. Personally, I'd be inclined to start a second one, in this particular case. Your first statement is quite strong, and a rush to the second would detract from it.
Is the end of the sentence OK, or should I add "ONE"? ...It boasts the oldest university in Scotland and the third oldest in Britain. ...It boasts the oldest university in Scotland and the third oldest one in Britain.