The most diverse big cities I've been to are Houston, Toronto, and Sao Paulo. The least diverse would be Moscow. If you don't have white skin (and even if you do), that place is quite frightening.
I've been to Moscow. It wasn't that bad though it was overpriced. But, the women were just great and that made it easier being there. That being said, a friend of mine who was studying abroad at MSU was assaulted by Neo-Nazis for being African.. so idk. Go to Vidor, TX or Macon, GA.. those places are really scary.