Wow, I can't say enough good things about either the lovely flat that Camila provides or the completely wonderful local hosting that Murat did. Even before we arrived, Murat gave us turkish instructions (including a note to call him) for us to share with a cab driver from the airport. Murat was at the apartment to welcome us and give us the basic story of the flat. He was very hospitable meeting us for a beer early in our stay and dinner later in our stay to talk about all kinds of things and help us understand a little about istanbul and Turkey. The flat is a lovely quiet respite from the chaos that Istanbul can be. There were a good set of cookware and we were able to prepare multiple meals in the flat. However there are also great turkish breakfast places right outside the door as well as numerous great restaurants, cafes, bars, etc just within a couple of blocks. This was one of the best airbnb's that I've stayed at (and I've stayed at a lot). I highly recommend it for a day, a week, a month.
If you stay, also please, please treat yourself to a turkish bath at Kılıç Ali Paşa Hamamı, just a 9 minute walk away.