If you stay in Sultanahmet, you will encounter a lot of overpriced tourist traps. Among these, Doy Doy stands out for being reasonably priced and having okay food. Of course it is aimed at tourists, and you won't find the tastiest food in Istanbul here, but it is good value for money given the district it is located in, and the food was fine. We had great service both times we visited, with a friendly waiter who was happy to offer advice when he had a spare moment.
On a Thursday night the upstairs was about half full. We ordered urfa kebap, beyti kebap, pomegranate juice, tea, baklava and sutlaç (baked rice pudding) and paid about 45 lira for it.
We also ate lunch on a Friday. It was not very crowded. We had kıymalı pide, kuşbaşılı pide and tea, for about 25 lira.