It's free and it's utterly absorbing, even for an Englishwoman with no known Scottish heritage. The Tower Restaurant in the roof is rather expensive but has one of the best views in Edinburgh.
www.nms.ac.uk/scotland/home/index.asp Chambers St, Edinburgh
Go see the Catfish (don't put your hands in though - munch munch!)
If you'd rather not pay for a meal to get the views from the Museum, there is a free rooftop viewing platform, which offers the same fantastic views for nothing...