Besides the Museum of Scotland there's the National Gallery of Scotland. I enjoyed visiting and learning about the Scottish Parliament. You probably won't have time to get up to Arthur's Seat overlooking the city, but Calton Hill would be another good choice. There's a Georgian house open for tours north of Princes St., I think it's called the Georgian House. Another interesting building, much older, is Gladstone's Land along the Royal Mile. That's all in Edinburgh.
In Glasgow, where I haven't been, I'd explore the Kelvingrove Art Gallery and Museum, and visit Glasgow Cathedral and the Necropolis. There's a transportation museum in a new building along the river. The Burrell Collection, south of the city, is supposed to be a very good gallery. And the Tenement House seems interesting, a place occupied by one person from 1911 to 1965 and preserved as she left it.