A great apartment in a great location, a friendly and attentive host is everything you need for a pleasant stay in the historical center of Istanbul.
An important plus is that a taxi station (24-hour office) is two steps away, from where it is both convenient and cheap to go to the airport.
Another tip: Hagia Sophia is open at night, when it is almost deserted. It is a 5-minute walk away, and you can go there as a walk before going to bed at least every day.
And Mr. Mehmet will be happy to tell you where to eat and where to go.