From Edinburgh Castle itself as far as The Worlds End bar (which serves a mean Aberdeen Angus steak) you can just feel the history all around you. This area is steeped in culture and history, some of it bloody and destructive.
The Castle itself is absolutely magical, and one would imagine it best suited in a childrens fantasy book rather then perched on a cliff overlooking a major modernized city. It's also very possibly the inspiration for the castle in Harry Potter as J.K Rowling actually wrote the first book in a little cafe called The Elephant Room only two minutes from the Royale Mile.
If you think the castle looks impressive from the outside then you should definitely take a look at the inside. There are some lovely gift shops just inside the main gate and is a good choice for picking up little mementos. The view of Edinburgh from the castle walls is not to be missed, and the view carries on as far as the eye can see.
My favorite room at the castle is in the center of the courtyard and is tecnically a large, beautifully decorated hall dedicated to every soldier that has died fighting for Scotland over the last 200 years.
On your way out don't forget to get a free sample of some of Scotland's finest whiskey. You'll need it to protect you from the harsh Scottish elements.
The Royale Mile itself is as you would imagine a dedicated tourist area with a variety of gift shops, bars, and restaurants. Don't miss it though as the buildings on this road are hundreds of years old and the architecture is world class. The world famous ghost tours also start on this street and don't leave Edinburgh without trying one as they are full of historical and cultural information, as well as being scary as hell.