We traveled to Edinburgh by train from London. While in Scotland, we took a hop-on and -off bus tour. There were several places we visited.
Edinburgh Castle and the Royal Mile
The castle is set on an extinct volcano and is instantly recognizable. The fortress is a World Heritage site and a powerful national symbol. The first time you see it from afar, nothing can stop you from visiting inside. When you are in the castle, you can see a breathtaking view of the whole city. The cafe at the castle has a reasonably priced lunch; you can go over to the window and see the royal mile below. Website: http://www.historic-scotland.gov.uk/properties_sites_detail?propertyID=PL_121 and http://www.rampantscotland.com/visit/blvisitroyalmile.htm
Scottish Wool Factory
When walking towards Edinburgh Castle there is a wool factory with various nicely priced wool items. I don't remember the name of the factory, but it was close to the castle.
This site is very similar to the London Dungeon. They are both very good. However, although the stories are different, if you have see one, you are not missing much to skip the other. Website: http://www.thedungeons.com/