My wife and I will be in Istanbul in October 2017 and are looking for some recommended apartment companies for a apartment to rent for 9 nights.
I usually use Airbnb for looking for Appartements in Istanbul, as the choice is huge
I stayed in Sultanahmet Suites back in June 2011 for over two weeks. There was a discount for paying cash (back then it was only 46 EUR per night, now it's probably even cheaper). I had a small kitchen and loved the apartment. Just be aware that there are actually three properties, although within 5 min or so walking distance to each other. No more than 10 min walk to the Blue Mosque and Aghia Sophia from there.