We just got back from Istanbul and want to share the best coffee and fish restaurants we visited. Both were recommended to us by a resident of the city.
Coffee:With your back to the catholic church on Istikal, look for a small alley way across the street to your right. There is no street name and the coffee shop is the second or third on the left (or, from the top of the alley, the second shop on the right.) It is a hole in the wall with only room for about six people inside. Most everyone sits outside the shop and it is the best coffee I have ever had, ever.
Fish:Off Besiktas street is a fish market surrounded by several restaurants. We ate at two of them and it was memorable.