History
Edinburgh has about 1500 years of history and probably the best place to get a handle on it is at the modest Museum of Edinburgh. Its good audiovisual display neatly sums things up. Another free museum is also worth a look immediately afterward: The People's Story helps provide an idea of what it was like to live in Edinburgh over the years.
And, if you have an interest or need a primer on Scottish History in general, then don't miss National Museum of Scotland, the country's most visited museum.