This apartment is very close to the Royal Mile, Holyrood Palace and St. Giles Cathedral. If you enjoy walking a bit (15 to 20 mins), you can also easily get to the Edinburgh Castle, Grassmarket, Arthur's seat, the Surgeon's museum, the National Museum of Scotland, the Royal Gallery, and Camera Obscura. A bit of a longer walk was the Botanic Gardens. Our group did not have a car and walked everywhere (all over 60).
I would highly recommend this apartment.