Hi there, I'm going to be as honest as I possibly can, and I apologize in advance to anyone I offend on the board, but I imagine it is inevitable. Moving to a new country is a huge step, and I feel like I owe as much of the truth as possible. Of course that it is the truth that I have experienced myself, so I won't be disagreeing with anyone who has had different experiences.
First, I have never ever had anyone treat me badly because I'm an American. Turks on the whole are very capable of separating politics from the individual. Of course, living in a metropolitan area, there are always rude people (I hate driving here!), but they don't share any extra-special rudeness with me =). Many are even nicer once they find out.
Now, as for being a Black American, almost every Turkish person I've ever met has claimed that Turks are not racist. Well....I'm from the South, and although I luckily never saw overt racism in my generation/town, I often felt its presence, bubbling under the surface. In Turkey, nothing bubbles under the surface. It's just out there. People may stare at you in the streets, not just because you are Black, but moreso because you are different. I have also seen cartoons in major papers where Blacks were represented as monkeys, and I've read ridiculous stereotypes in print. This is racism to me, but not particularly troubling to anyone I've discussed it with here. They have commented that such things are silly or unnecessary or ignorant, but their reaction was nowhere near mine. You may also be asked silly questions that are not meant to offend you but are mainly based on watching too many stereotypical Black characters in the American media. It is akin to the people here who assume that as an American, I have no cuisine and only eat fast food. Simple ignorance, but not malicious. Such things really are not personal in Turkey and do not relate much to how you will be treated as an individual.
If you can just treat the occasional ignorant actions or questions as opportunities, or ignore them completely, you will probably love Turkey. Most Americans do, whatever their race. I have found Turks on average to be very friendly people, amazingly loyal and protective of their friends. You have to try hard to be lonely here. It's just not allowed =).
I know I've written a lot, but I do hope it helps you. If you decide to move to Istanbul, feel free to email me. It is a wonderful city, and there is no other like it as far as I am concerned. Turkish coffee, my treat, to welcome you!