And now something completely different, as Monty Python was wont to say.
Spend your two days going down the west side of Scotland. See Loch Ness and its Monster. See Glen Coe, one of the most beautiful places in Scotland, if not the world. Stop and play golf at Fort William at the foot of Ben Nevis, which was a cow pasture when I last played it in 1981, but oozing potential--it has now apparently mellowed, please report back! Maybe even play Colt's 9-holer at Fort Augustus (if it is still there). Then go past Loch Lomond, another bit of world-class eye-candy (the loch not the golf course). Spend a few hours in Glasgow, shopping, drinking, trying to understand the natives.
All these are within a half-mile of the A82 (the main road from Inverness to Glasgow). At the very least, you'll see parts of Scotland that 95+% of the visiting golfers never see.
Regardless of what you do, enjoy.