The flat was as beautiful as described and is perfectly located. The bus stop is a 2-minute-walk away and gives you 3 options to get to the centre. A taxi ride will cost you 8 pounds.
The neighborhood is perfect for a quiet timeout from the city's trouble. The supermarket, which is a 4-minute-walk away, will satisfy all your needs. The restaurants near to the flat are absolutely recommendable and the pubs of course, too. You will reach the Botanical Garden in 15 to 20 minutes on foot and the beautiful Walk of Leith (Dean Village) in 10.
Finally i must say that Neil's a cool host who took the time to give us some recommendations. If you want to spend some time in Edinburgh, do it there.