After flying in international business class to get to EDI, we spent three wonderful days walking around the old city; absolutely not enough time, and we both badly want to go back soon!
For anyone finding themselves in the area, Mary King's Close is absolutely worth the tour. It's a few blocks of the city from the 17th century, formerly left forgotten and preserved under the Royal Mile. Learn from my experiences, reader: don't go in the haunted room with the ghost girl. Emily insists I got haunted—I insist I got food poisoning. Regardless, take the tour but don't go into that room.