My family visited Scotland in 2009, visited relatives in Ayrshire and went to the Open at Turnberry. While we were there we played some fun and interesting courses. Summer days are long in Scotland so you can tour and golf in the same day. You might want to look at these “non-premier” courses for a different experience/extra round.
Dundonald Links – played very late in the day and had course to ourselves. Wife walked with us.
Belleisle Golf Club – Beautiful public golf couse and wife walked with us.
Shishkine Golf & Tennin Club – very short course on the West coast of Arran and only 12 holes. Took ferry over from Ardrossan and made a day of it
If you make it over to Edinburgh you might want to consider:
Prestonfield Golf Club – Just south of Edinburgh