I highly recommend staying at Alison and Johns flat in Marchmont. Both the flat and the neighborhood are great. I really enjoyed walking around Marchmont and Bruntsfield and Morningside. These neighborhoods have great coffee shops, bakeries, restaurants and pubs. It's also a great walk to go from the flat into the New Town. I walked north across The Meadows, through George Square, along George IV Bridge to The Mound which has great views both north across the New Town and south to New College and the Castle. I continued walking north into the New Town and ended up wandering into Stockbridge, stopping at several shops and pubs along the way.
It also turns out that it's easy to hop on a city bus very close to the flat and get anywhere in town.
Their flat is really comfortable and cozy. The bed is super comfortable. The bathtub is luxurious. And they've got great fluffy towels, which I appreciate. The living room is cozy for hanging out. And the entire flat is really quiet.
It's a great home base for exploring Edinburgh or to have a quiet home in a nice neighborhood to stay if you're in the city for a business trip.