Alegrias1
Nobody's mentioned the Castle! Followed by a walk down the Royal Mile.
Another vote here for the National Portrait Gallery. Also the National Museum of Scotland.
Me, I'd give the Britannia a miss.
I second the museum. One of the most amazing museums I’ve ever been to and I’ve been to lots. Quite difficult to find initially, though, although I’ve worked out where it is now. However it will take up a whole day of a two day visit: there’s so much to see! I also have to make a pilgrimage to Greyfriars Bobbies statue and the Kirk yard and cry every time I get there! And I went to the modern art gallery last time I was there and loved it. I think there’s a shuttle bus that takes you to all the different art galleries. However, if you’re only there for a couple of days I guess it’s best to do the bus and get a feel for the place. I’ve yet to see the sea at Edinburgh and forget it’s actually on the coast. The train ride from Berwick to Edinburgh is wonderful, too. And Edinburgh Zoo.