Ben,
I started my only trip to Scotland by getting off the plane and driving directly to play 36 on Gullane 2 and 3. It was a wonderful introduction and the visitor clubhouse, while probably not as steeped in history was perfect as it had lockers and a shower which were nice to have available.
I loved the courses and heading up the hill and then seeing the views, it is a lovely place. I wanted to play Gullane 1, but they had competitions the one day I had available, and I'm glad I played Gullane 2 and 3, they were a lovely way to spend the day. I played as a single and every group I met was kind and chatty as I played through.
Here is my breakfast view.
And the amazing sky the day I arrived.
I also played The Glen Club as a single before my round at North Berwick and enjoyed it. It was a picturesque morning spot and nobody was there. The pro was kind enough to let me out before play that day, and it was greatly appreciated. I loved Kilspinde and am very envious of your trip. Here are a few from there.
I've not played Luffness or Musselburgh, but that region seemed particularly blessed with great courses and imagine they would be lovely to play.