A friend of mine here in the US was born in Istanbul and visits his mother who lives there. He quite the foodie and was kind enough to share a number of recs. Not all are about food but enough that I think this is worth sharing here.
"1. SULTANAHMET KÖFTECISI !!!
This is the lunch stop for the day you see the Hagia Sofia and the Blue Mosque. Please don't be swayed into any other place. It's essentially across the street from H.Sofia and the hippodrome remnants. A "köfte" is a small Turkish grilled meatball. This place has the best in the city. Even though its touristic, and been that way for decades, it's still the best and my mom and I go there to this day. FYI, I order a double portion to start. Their desserts are also great.
2. The Cisterns.
If you don't have this on your list, make sure you amend. It's also in the old city neighborhood and is unmissable. It'll take less than an hour - it's underground, fascinating, beautiful.
3. Breakfast or Brunch at either of the 4 Seasons hotels. Yes this sounds distinctly un-Turkish, but the two hotels are both special. The first used to be a political prison and now the old courtyard where the inmates would pace is a garden where one frolics and dines. The new hotel is right on the Bosphorus and that view is unmissable. And for a cost, you can dine very well at 4 seasons. :)
4. Galatasaray Adasi, aka Kuruçesme
Amazingly, this is a tiny little island in the middle of the Bosphorus with 5 restaurants! Amazing venue. You can only get there by ferry. Great food and ambiance. I'd do lunch.
The clincher is that I learned to swim on this island, and the huge pool (which is filled with saltwater rushing through the strait) is still there, with the restaurants perched around it. It used to be a sports facility when I was a kid.
This is a Turkish ravioli dish that you must eat as much of as possible. Your hotel will tell you where the best closest place to find it is.
6. TAVUK GÖGÜSÜ (pronounced taVOOK guhewSOO)
This is a dessert dish that you must try at least once. Ask what it's made of AFTER you eat it, if you trust me. Research it if you don't - but still try it!
This is also a dessert - usually served on top of other desserts but also eaten on its own. It's essentially the heaviest cream ever. Few tourists try this incredible stuff. My mother lives on it.
8. Döner sandwich
You've had shawarmas, gyros etc. PLEASE eat a Döner sandwich or 6. They are the last word in twirling meat column slices in bread.
9. SARAY MUHALLEBICISI.
Good luck pronouncing that one. This is an old old chain of restaurants that was "classic" when I was a kid. It's a catch-all for numbers 6, 7, and 8 above. You can find them in other places just fine, but if you see a Saray Muhallebicisi (they've branched out), it's döner, kaymak and tavuk gogusu are great.
A great little place for little gifts. Jewelry, pottery, handmade stuff, art, rugs. But most importantly, it's stunningly beautiful. Right on the water with a great old mosque pushed out into the strait. There's a square with little restaurants and cafes where you can grab a cup of tea and people watch. Finally, ferries take off from around there, and there's nothing risky about jumping on a ferry randomly to see where it'll take you, or just ride it until it brings you back to where to took off.
You should definitely take a ferry SOMEWHERE. The city used to run on ferries before the first of the two big bridges between the continents was built in the 60s. The second one was built when I was in 3rd grade and we had a field trip on it.
12. Beyoglu - Galata Tower
Beyoglu is a pedestrian walkway that connects Taksim to Galata. A great promenade on a sunny day is to walk all the way down Istiklal st (the street that makes up Beyoglu) and find the Galata tower within the warren of little streets at the end. Climb up the tower for an unparalleled view of the golden horn, and read the history and legends of the tower.
13. Ciragan Palace - gosh I hope you're staying there. ;)
14. Hagia Irene
A much smaller church than Sofia. If there's a concert at this church when you're there, try to go! It's now a museum and concert venue and its such an amazing space. The concerts are usually short and sweet, good evening thing to do.
15. ÇIÇEK PASAJI
Aw I love this little thing. It's on the Beyoglu walk down to Galata Tower. Incredible little place to grab some grub - Very Authentic. The architecture is from the art nouveau rebirth that Istanbul enjoyed. Great restaurants for Meze style eating - like tapas. If you decide to brave "Raki", this is the place. It will get you very drunk.
I'll end with a very special dish. LAKERDA is a fish that you must eat. I just looked it up and Wikipedia says its pickled bonito, which I didn't even know. It's usually served with raw red onions and lemon, and my mouth is watering right now and I must go eat dinner."
He made OUR mouths water also. Leaving in less than a week. YAY!!!