As the other reviewers have said, this is a brilliant flat right perfectly located in the middle of the old town, but remarkably secluded and peaceful. It's good value in an expensive city. The flat was super clean and comfortable, actually more spacious than I was expecting from the photos. The local host company's communication and response was very good. We would definitely come again.
Tip: There's a convenience store just across the Grassmarket square where you can pick up a few groceries. The Google reviews of that place suggested it was overpriced, but it didn't seem too bad.