Terry,
It sounds like your trip will be much like my maiden voyage across the pond. We started out down in England at a GCA gathering, then I headed solo up north. Started at Murcar, then on to Dornoch (36 holes there is a must, and Stan Dodd is outstanding company), Cruden Bay, TOC, Elie, North Berwick. Dornoch, North Berwick, and TOC are the must plays, everything else is gravy and there is plenty to choose from. I don't know what sort of accomodations you are looking for, but for the budget-minded I found three hostels on this trip that were all owned by the same company and all were very much worth the 12 pounds. The locations are Inverness(perfect location for the trip up to Dornoch from Aberdeen, one in St Andrews, and the last in Edinburgh. You really can't go wrong on your first trip to Scotland so just enjoy it. Don't worry about the naysayers who think you should hunker down and just stay in one area. I had no problem getting around between rental car and trains. Rental car from the Aberdeen, Dornoch, Cruden Bay loop. Train the rest of the time.