Stayed here with all my family this September and it was a very pleasant stay. Firstly the apartment is spacious and fit us - 9 adults (and kids!). Also it is very conveniently located to all the major sites. Yes one route to the Blue Mosque/Grand Bazar requires a lot of up hill and down hill walking (which although we managed I can imagine it would be hard for those with children/the old/Pregnant). Thanks to Google maps (download the route at the apartment as we would do) we found another route that took us 22 minutes to get to the Blue mosque. It went through the quiet and bustling streets of the area, past the Kumpkapi fish restaurants, through Sokollu Mosque and right up to Blue Mosque (all other sites are nearby). This walk is much more pleasant and not steep and for the rest of our stay we took that route only.
The apartment location is a bit off the beaten track but we felt very safe here during the night too as the locals are very friendly and the surrounding shops do have some good bargains. Unlike Sultanhmet this place is alive during the evening and we could really experience the local Istanbul life.
Enes's Dad AbdulBaki is absolutely great and took us to see Bursa/ and to see Istanbul (namely key Islamic areas at a very reasonable price. He went above and beyond and we were very glad to meet him.