Glamis Castle - Queen Mums vacation home. It was absolutlely gorgeous and fully furnished. Sterling Castle was nice as well, but Glamis was better.
We also went to a local distillery and saw the making and producing of whiskey. It was quite interesting.
St. Andrews was quite a sight. On Sundays the course is closed off to players and people can walk around it or let their dogs run wild.
William Wallace monument is a must. You get to drive through braveheart country and see where it all began.
Quick Tips:
If you don't try any other scottish fare - hagis is a must. Not because it is fabulous, but just to say that you tried it. It tasted a lot better before I found a recipe with the ingredients.
Best Way To Get Around:
We did tours that our resort recommended. It was far safer than driving. There were many US citizens getting into car accidents and we felt it was safer to not drive.