Riding the subway means that as a white New Yorker, you will twice a day share a room with a black person. Whether you interact with them is another story - I'd venture that most people never say a word to anyone in the subway. To understand (likelihood of) interaction, neighborhood maps are one piece of the story, as would be (as mentioned elsewhere in the thread) workplace data.
But you are also likely to live in the same neighborhood as your friends. So while living in a racially diverse neighborhood may not cause you to interact with people of other other races, it may be indicative if your group of friends is racially diverse.