Go to www.nationalrail.co.uk/stations_destinations/maps.aspx . to view the Scottish rail routes. You

I was thinking we'd fly into Edinburgh and spend 3 days there, pga tour golf clubs maybe doing some day trips with Rabbie's or another local business, then travel to the Aberdeen area for a day or two, Nairn for about 2-3, the Isle of Skye for 2-3 days, and wrapping up with Glencoe (back to Edinburgh to fly home). Are all of these locations stops on the system? Once we're in the towns/cities, is traveling around easy to do?
Nairn is an easy train trip from Aberdeen. Skye by train is more complicated. You'll need to go via Inverness to Kyle of Lochalsh or go via the West Highland route from Glasgow. Both are especially scenic routes; however, I wouldn't recommend Skye without a car. It is possible to get a driver for tours around Skye, but it can be expensive. Since you mentioned Aberdeen, there is an overnight ferry to Lerwick, Shetland. There are a couple of companies that offer a variety of tours around the islands.
Go to www.nationalrail.co.uk/stations_destinations/maps.aspx . to view the Scottish rail routes. You need to factor in travel pga tour golf clubs time when planning your itinerary. You can do this at the national rail site. Also look at the Scottish Rover Pass. It may or may not save you money.
Of course, I forgot to mention that the West Highland route ends in Mallaig where you then need to take ferry to Armadale on Skye. Train terminates at Kyle of Lochalsh pga tour golf clubs and you will need to take bus or taxi across the bridge to Skye. Thanks janisj for pointing this out.