It certainly is doable. Many years ago a friend and I drove from Ayrshire (SW of Glasgow) to Inverness via Loch Lomond and Loch Ness, spent the night in Inverness, then drove to Aberdeen via Elgin and Fraserburgh. It was an enjoyable 2 days that I do not recall as being rushed, and looking back on it I also do not remember anything I regret that we missed seeing. What I remember from the trip are our stops at Castle Urquhart, the ruins of Elgin Cathedral (which I recommend), Fraserburgh (where we visited friends for lunch and tea and enjoyed strolling around the docks where the fishing fleet was), the Bridge of Don in Aberdeen, and Dunnottar Castle (south of Aberdeen). I think we found the B&B where we stayed by going to Tourist Information in Inverness and were very happy with it. This was in early August - but like I said, quite a few years ago.

So if you have 10 days you should be able to do the drive. The key will be deciding what you want to see and how much time you want to allot to it. Glasgow is worth visiting, which easily could be at least a couple of days. So is Culzean Castle (pronounced "cull-ayne") in Aryshire (near the famous Turnberry golf course) - and Ayrshire is Burns country as well. And the late afternoon light on the beach and the stone buildings in Troon was magical when we were there.

As far as planning goes, I would start with what you know you want to see and decide how much time you want to spend each place. Don't worry at that point how much total time it adds up to. Then plot out where everything is on the map, and start adding to or cutting from your itinerary so it fits the time you have.

You can use a mapping site like Google Maps or http://www.theaa.com/route-planner/index.jsp to give you an idea of driving distances between places.

http://www.secret-scotland.com/
have a look at this website,they can help you plan a tour including all the things you want to see and give a general itinary and suggestions on where to stay.They do charge a fee but it may be worth in in your case.

You could go to Hadrian's Wall as a day trip from St Andrews. Head for the Forth Road Bridge, take the City Bypass around Edinburgh then the A68 south, then onto the Military Road at Chollerford for the Wall itself.

The A68 crosses the Wall on the Chesters area but you might want to see Vindolanda and the area round Steel Rigg.

As for your tour, I'd suggest heading out to Skye on via Fort William & Mallaig, cross using the ferry spend a couple of days there then cross the Skye Bridge and head to Inverness. From there you can reach John O'Groats (not really worth it BTW) or take a ferry to the Orkneys (well worth it). Then return down the east side either through Royal Deeside or by the Cairngorms back to St Andrews.

Thanks for your good suggestions and positive response to the idea. It is hard to understand the scale of things. We did not drive the last time we were in the UK but took tours to the Loch Lomand & Ness areas. I shall continue my research based on your ideas/suggestions.