Dundee has RSS Discovery
http://www.rrsdiscovery.com/index.php?pageID=129
I've been on it.
Glasgow - Science Centre (been there!)
Edinburgh - Castle, Scot Monument, Royal Observatory - seen them all.
Stirling - Wallace Monument
Bannockburn - battle site/exhibition
Inverness - Loch Ness
Culloden - battlefield site/exhibition
Aviemore - the Cairngorms
Tomintoul - more of the Cairngorms
Braemar - Glenshee, Balmoral Castle
Orkney - prehistoric sites
West Coast - the islands
Plan your route carefully to make best use of your time. No motorways north of Glasgow and Edinburgh - A9 to Inverness, A90 to Aberdeen are fast roads.