Our family had a great stay at Aslan Apartments. The duplex we booked for 5 of us was well equipped with beds, linens, cookware, and some very thoughtful food supplies that were a big help to us jetlagged people who speak no Turkish. The apartment is on a residential street (both quiet and really a part of the city, which is chock full of tourists in other places) but also steps from markets for everything from food to souvenirs, restaurants, and major sites. Our hosts booked our transportation in and out of Istanbul, which was also extremely helpful and worked perfectly.
We especially have to thank Gulnur, Aslan, and the housekeeper for coming to our rescue at 5am on the morning of our departure, when we locked our passports inside the apartment. We're sorry (and as Airbnb hosts ourselves, appalled at waking them up at that hour) and couldn't be more appreciative of how graciously and quickly they solved our problem.
This is a great place to stay and we totally recommend it.