Just came back from a 17-day trip through Scotland with golf as a major component. If you'd like to play a great course and give yourself an opportunity to wander around Edinburgh, go to North Berwick and play the West course. Second oldest essentially unchanged course in the world (behind the Old Course in St. Andrews). It's fantastic, a real challenge, and has been used as a qualifying course when the Open has been played at Muirfield and St. Andrews. After playing, you can jump on a commuter train from the North Berwick train station about four blocks away into Edinburgh which takes about 30 minutes and drops you off at Waverley Station in the heart of the city. Trains run frequently through the day so you could easily spend a couple of hours in Edinburgh--certainly not enough for this ancient city but it might give you enough of a taste so that you'll want to return on a future trip--and then catch a return train to North Berwick to continue your journey. Or if you want more golf, just go to the other side of North Berwick and play the Glen course, which I consider an excellent introduction to seaside golf in Scotland and, depending on the time of day, can cost 1/3 to 1/2 of the greens fee at the West course.

In Fife, try to carve out time for the Balcomie Links at the Crail Golfing Society and the links at Elie. By the way, if you want to try getting into Edinburgh from St. Andrews, trains frequently run from nearby Leuchars into the Haymarket and Waverley stations. Longer ride, closer to an hour, but running across the Forth railway bridge, giving you a chance to see the spectacular scenery without the bother of having to navigate a vehicle.

If this is your first trip to Scotland, a superb resource for the traveling American golfer is Allan Ferguson's Golf in Scotland. I've done six trips to Scotland, and I can heartily endorse just about every piece of advice he gives--especially about seeking out open competitions and the various methods for getting on the Old Course. Buy the electronic version--it's cheaper and can be read through Kindle or Nook apps on a cell phone.