In St Andrews you can get a guided walking tour of the old course. We actually only walked 3 holes.
Check out the St Andrews Cathedral cemetery and and see Old Tom Morris' grave.
Train to Dunfermline Abbey. Robert the Bruce's tomb is in the Abbey. as is a shrine to St Margaret.
Tour HMY Britannia
Stirling Castle is a must.
From Inverness, day trip to Culloden
https://www.nts.org.uk/visit/places/culloden
Visit Speyside Distilleries
Here are a few more , we did not visit all of them
Edinburgh
Top 13 Must Do Activities when visiting Edinburgh
1.Edinburgh Castle , Castle Hill, 0131 225 9846
2.Royal Botanic Garden , 20A Inverleith Row, 0131 552 7171
3.Museum of Scotland , Chambers Street, 0131 247 4422
4.Camera Obscura and World of Illusions , Castlehill, The Royal Mile, 0131 226 3709
5.Royal Yacht Britannia , Ocean Terminal Leith, 0131 555 5566
6.National Gallery of Scotland , The Mound, 0131 624 6200
7.Scott Monument , Intersection of Princes Street and Waverly Bridge, 0131 529 4068
8.Royal Mile , Edinburgh Castle to Holyroodhouse Palace, Old Town
9.Holyroodhouse Palace , Holyrood Road, 0131 556 5100
10.Real Mary King’s Close , 2 Warriston’s Close, High Street, 08702 430160
11.Open Top Bus Tour, Waverley Bridge, 0131 220 0770
12.Museum of Edinburgh , 142 Huntly House Canongate, Royal Mile, Edinburgh, EH8 8DD
13.John Knox House
Check out the attached PDF