If you are not planning to rent the Hagia Sophia, you cannot really stay much closer to the middle of the old town.
Everything is in walking distance (10 min) Bazar, Mosques, Topkapi Palace...
As a bonus you have access to the roof of the building with stunning view over the city.
The location is accurate, you can get and leave the keys in a nearby hotel so no issues checking in and out, if you drive or rent, you will have some trouble finding a parking spot, but there are parkings in the area.
The ap gets rapped up every day by room service also.