Be careful, carry your passport, and avoid the police. This advice does not only apply to those from racial/ethnic minorities, but it is sadly more important as one is more visually distinctive from the majority. This is particularly the case if you are in Moscow around the May holidays, when there will a significantly increased security presence. I would be surprised if there were overt harassment, but even as an American I would expect that, given the chance, your documents will receive significantly greater scrutiny for any potential problems. Contrary to the usual advice to tourists, if you look more American I would expect fewer problems.