There are two main castles in Edinburgh - Edinburgh Castle and Holyrood Palace. Edinburgh Castle is more in the center of town and virtually impossible to miss, as it sits at the end of the Royal Mile. In addition to offering some good historical information, it provides a perfect view of the city. Holyrood Palace is not quite as impressive but still worth a visit. It is a slightly longer walk, though still quite manageable.
Arthur's seat is at the top of a large hill not too far from Holyrood Palace. The hike up is great for those wanting something a bit more active, and it too offers a sprawling view of the city.
Edinburgh is known to be one of the most haunted cities in the world. They offer a number of ghost tours, the scariest being the night tour that takes guests into the underground tunnels of the city. The tours are both historic and thrilling, and unlike many ghost tours, they are strictly factual - no hand crafted ghosts and goblins jump out at you as you walk. This is one of the "musts" for any visitor who feels they can handle it.
Scotch Tour - Though a bit cliché, the whisky tours and tastings do offer a bit of background about the making of scotch, and if nothing else, you get a free glass at the end!