Carnoustie - hard but not overly hard until the last four holes. If the wind is blowing, disregard the previous statement as it will be tough no matter what. Great course and a must play in my opinion.
Kings Barns - outstanding course only 15 minutes from the town of St. Andrews. Relatively new course having been built in the last few years. Beautiful, beautiful, beautiful and very tough. Not a typical Scotish course but one of the great courses in the area.
St. Andrews - Jubilee - in my opinion, the hardest course at St. Andrews. Brutally hard. We played it in a 35-40 knot wind and some of the holes along the coast were unplayable. I'm a sub-five handicap and I hit the ball well and was pleased to shoot a smooth 100 out there. Tough course and the wind (which always seems to blow) makes it insane.
St. Andrews - Old Course - yeah, you said not to mention it, but to not mention it on a thread about Scottish golf courses is sinful. Do whatever it takes to play this course. If you don't have a tee-time, and don't make the ballot, show up at 4:30 in the morning (I'm not joking) and get on the singles waiting list. My dad and I showed up at 4:45 the last day we were in Scotland (we missed the ballot five times... unheard of) and we were the third and fourth people in line. We resigned ourselves to playing in different groups but cheesed out and got to play together with a twosome that was willing to let us play with them. Best experience I have ever had or will have on the golf course. The course is everybit as amazing and difficult as it appears on t.v. Great memories and the best caddies you will find.