It was October when we were in Turkey and palamut (bonito) were available in every fish market. I suggest you walk across the Galata bridge to the fish sellers that line the shore. There are several open-air restaurants along there where you could get a very simple meal. Some of them are better than others, but you can get a pretty decent idea of who has fresh stuff just by looking around. Very cheap.
Of course, there are quite a few fish restaurants in the Kumkapi district as well, but we found them relatively expensive and filled with package tourists. Prefer the street-food approach.