The Sultan's Inn is in the center of Sultanahmet. Within walking distance of Topkapi Palace, Sultanahmet Mosque, the Hagia Sophia, the metro and a taxi rank. The Doy Doy restaurant became our dinner spot- good food at reasonable prices. Recommended by the staff here.
We had a terrific breakfast each morning looking at the mosque just above us.
It is value for money. They will arrange airport pick up and drop off, too.