Looking for the best kebab in Istanbul is like searching for the best spaghetti or pizza in Rome. There are bunch of places doing really good kebabs. If you want to go local, I suggest you to try kebab restaurants around the Grand Bazaar area, such as Şeyhmus Kebap. Şeyhmus is a typical kebab lunch place among the local people.
An other great place close by Taksim Square, city center of Istanbul, is Zübeyir Ocakbaşı. I personally claim that Zübeyir is one of the best kebab restaurants in the town. I recommend you to go to Zübeyir for dinner, although don't forget that reservation is essential.
SUR KEBAP in Fatih is one of the best kebap house in İstanbul
I have been to almost all the kebap places Develi Kebab Samatya is simply the best place in İstanbul to have a kebab without an alternative. Also kuru patlıcan dolması, (stuffed dried eggplant) and gavurdağı and a lot of things I cannot name at the moment since it feels strange just even writing about them. I'm hungry.