Dynamic Earth right between Arthur's Seat (as seen in the background) and the buildings of the Scottish Parliament. Visiting it is rather expensive in comparison, but worth doing it once in my opinion.

There's an aquarium at North Queensferry called Deep Sea World a short trainride and walk away from Edinburgh. If you look back at the former picture shot out of the train running the bridge, it would have been just outside the left side of it. Down below the cliff you could see a part of.
It's not very big, but certainly worth a visit. Housing a number of seals as well, both permanent residents and injured ones that were rescued and are being nursed back to health.

There's a small, stairway-filled alleyway running up from Waverley Station into the old town of Edinburgh and to the Royal Mile, the Fleshmarket Close. The Halfway House pub lies about, well, halfway up the close.

George Heriot's School between Edinburgh Castle and the National Museum of Scotland as seen from Castle Rock. It is said that its design at least partially inspired Rowling as to the looks of Hogwarts.

The Camera Obscura not only features its namegiver, but several floors with optical illusions of various style. This alleged corridor being one of them. From the markings you can make out, some people seem to have tried walking it.