Do a search on this board and you'll find several threads about Istanbul. We were just there in the fall and, to be honest, I can only give you one bit of advice. You won't necessarily get much better food in more expensive restaurants. You will likely get better service and presentationand the view will be awesome, but this doesn't always translate into a great chowhound experience. Our most memorable meals were in very simple places that appeared to be populated with Turkish people. If you're looking for good inexpensive fish, avoid the "fish reataurants" that cluster in tourist areas. If you want to eat good kebabs, go to a simple kebab shop that does NOT have a fancy display in the window and menus in eight languages. Eat street food. Eat market food. Eat pide freshly baked in front of you. Visit those scary steam-table buffet places (some interesting dishes there).
Don't ask your hotel where to eat. They will send you to the Kumkapi district (fish restos) where the meals will set you back close to $30 per person - which doesn't sound expensive except that you can eat so well so cheaply elsewhere. You may have better luck that we did asking for advice - maybe you can really get across the fact that you're looking for GOOD FOOD not FANCY FOOD (if that is, indeed, what you want). Ask them to send you where the locals eat. Turks are very hospitable and want you to have a wonderful time so they may be reluctant to suggest a simple restaurant unless you insist that is exactly what you want.
We enjoyed wonderful meals in funny out-of-the way places that I don't even remember the name of and could never find again if I wanted to.
One more warning: Turkish wine is pretty uniformly awful. We drank it, of course, because I just wanted some wine sometimes but it was the type of swill I wouldn't touch at home.
An alternate point of view on the Kumkapi fish district: It was near my hotel and I went alone on my last night in Istanbul. I checked out all the restaurants and chose one (Neyzen) that seemed to have no tourists, certainly no groups. I knew bluefish was in season and asked if it was fresh. The waiter took me to the back of the restaurant, showed me the fish swimming in a tub, and asked me which one I wanted. I had the ubiquitous white paynir as an appetizer with the equally ubiquitous Raky (for which I had developed quite a liking) and the perectly grilled bluefish all for about $20. For me at least, it was a perfect last night in Turkey, and one of the best meals I'd had during a one-month trip.
I'm with you, Raki and Blue fish -- it doesn't come any better. What is translated as Blue fish in Turkey should not be confused with our East coast Blue fish (which I also love).They are two different animals. In Turkish Blue fish is called Lufer. It's truly one of the great eating fihes of the world. Depending on size an order might consist of 1,2 or even 3 fishes. Enjoy!
Nyleve is right on the money here....I lived in Istanbul for a year in the mid-90s, and my fave place in all of Istanbul was a small neighborhood kebab shop right around the corner from my home in Besiktas (pronounced Besh-ick-tosh) called Hazal Ana. Although they were just a humble place specializing in iskender kebab (grilled lamb doner on pide bread topped with a spicy tomato sauce, thick yogurt, and browned butter ladled on top), service was superb - they treated me like a king and served up great grilled dishes of all sorts every time I went. Their various pide breads were cooked fresh out of the oven, and amazing - when I had my last meal there, they even made me a special one with my name on it in black sesame seeds! Incredibly sweet folks, and the fact that it's incredibly cheap is icing on the cake...I always left HUGE tips because I loved them so much.
Bear in mind it's totally local, so there's probably no menu or anything in English, and they didn't speak much at all either (I believe a third party delivery service link with a menu in Turkish is here: http://istanbul.aloyemek.com/Restoran.aspx?sube=523). I think it was BYOB too, but there's a small wine/liquor store nearby if you look around if they don't have anything behind the counter and you have a raki jones on.
Besiktas is about 10-20 mins from the Taksim area, easily reachable by taxi or a dolmus minibus. I don't have their address, but it's in the bottom floor of a triangle shaped building at the foot of Serencebey Yokusu, a few steps up from the intersection of Besiktas Caddesi, Ciragan Caddesi, and Barbaros Bulvari (see map below, it's close to the center).
If they're as good as they were back then, I would make it a point to try to stop there and enjoy a lunch or dinner after a Dolmabace palace visit. Just order whatever looks good, be sure to get a nice Turkish dessert and/or coffee afterwards, and you won't regret the side trip!
TIP: you may want to avoid the "cig" kofte appetizer they may give you there and in other restaurants if you have any sort of weak stomach. "Cig" (pronounced "chee") means raw, and it's basically a spicy steak tartare. It's actually REALLY tasty if you like that kind of thing, but my system never quite got used to the spices anytime I ate it anywhere (the meat was absolutely fine), and I ate it a lot.
BTW, aother place I really liked for a quick snack was any of the half-dozen doner kebab shops right at the mouth of Istiklal Caddesi in Taksim, next to the Marmara Hotel - all were good any time of the day, simply pick whatever looks tastiest, and choose whichever kind of bread you want (you can get 'em in a lavash or a standard pide). I practically ate lunch there every day rotating between each and getting to know the guys who ran them. Many offer fresh squeezed juice drinks, too.
And if you're feeling decadent, travel further down Istiklal for dessert at a crowded place called Saray Muhallebicisi, and again pick whatever looks good, because all of it is. And if you order a jellylike sweet milk pudding called tavuk goksu and find bits of chicken in it, don't worry - it's supposed to be in there (and it's quite tasty too!)...here's a good link about 'em:
Turkey is full of great things to eat...I could go on and on about it, but I'll stop here at these highlights. Enjoy your trip!