I totally (and personally of course) agree with Kemal.. There are beautiful small boutique hotels at Sultanahmet region (hippodromme). The thing is it would be good to have some references about the quality of the service at the hotel to stay in.
Because the facility may be "handsome looking" from outside but what happens if you are disappointed with the quality of the service when you check in.
I would personally like to suggest one which belongs to a very good friend's sister (very disciplined and successful business lady and all). It is called the Arena Hotel. I will put links below. It was made into a hotel form a former Ottoman House and all and it reflects tradition. Moreover you can find traditional Turkish food (from hygienic and clean kitchen .. which is a very important thing to look for in Turkey especially)
http://www.arenahotel.com/
you can watch a video about the hotel in this link
http://www.videosofturkey.com/video_details.asp?id=100