Stunning flat near St. Giles' Cathedral

We've stayed in two of the apartments on separate visits and liked both. They had similar, good layouts and furnishings, with two bedrooms, a kitchen, and a living and dining room. They're clean, and the building is actual residential space rather than a hotel. There's no AC. Registration happens down another nearby close, which seemed odd at first but is completely legitimate. Just off the Royal Mile and close to Giles Cathedral, the apartments are halfway down a large close, or alley. Nearby are a BBQ wings place, a cafe, and a trendy bar, so there's food, drink, and some noise. A ghost tour also stops in the close outside. We'd definitely stay here again in Edinburgh with friends.