I have assembled the following restaurant list from a few guidebooks and the forum. I'd be interested in hearing how other travelers might have felt about these restaurants and recommendations for any others. We tend to stick to midprice unless something is really special:
$$$$OCAK, Hobyar, No:5 | Regie Ottoman İstanbul Hotel, Mimar Vedat Sk., 34112 Fatih
$Forno Balat, (RS) Vodina Caddesi at Fener Kirechane Sokak 13, tues-sun, 10-20 (Balat Neighborhood)
$$Sehzade Erzurum Cag Kebabi (RS), Hocapasa Sokak 4/6, 11:30-21:30, by train station
$$Siirt Seref Buryan Salonu, (RS) Near Suleyman the Magnificent, Itfaiye Caddesi 4, 11-22
$$Hamdi Restaurant (RS) near Spice Market, Kalcin Sokak 11, 11:30-23:30, good views from balcony
$$Lekker Café Restaurant, Forum recommendation, No. 7 Sultanamet Fatih, mixed recent reviews
$$Imbat, Hudavendigar Cad 34, lamb, reserve ahead for Bospherus view
$$Pasazade, Ibn-I Kemal Sok 5A