I killed a good half hour playing with this racial diversity dot map. It visualizes some of the spatial racial distribution of cities that you can only intuit from ground level as a resident. While a city may seem quite integrated and diverse, it isn't until you zoom in that you see that what looks like a diverse blob of people is really a series of segregated neighborhoods.
One personal hunch, though, is that how diverse a city feels is not just based on how segregated the population is based on their place of residence but how much those populations interact in day to day life, and that is a function of city density and the developmental maturity of the city's public transportation. While New York City looks like Chicago or San Francisco or other big cities in being a collection of segregated neighborhoods, it felt like the most diverse city I've ever lived in because those populations crossed paths on the city streets and subways every day in high numbers.
Thomas Schelling's Segregation Model, one of the more powerful agent based models I've ever studied, shows how the extreme segregation of American cities might arise from much milder racial preferences. It's a critical model to study, one that is useful to keep in mind when trying to avoid a variant of fundamental attribution error when trying to explain how something that builds over time ended up in a bad state.
This report (PDF) from 2011 studies long term racial segregation trends in America and comes to this conclusion:
The 2010 Census offers new information on changes in residential segregation in metropolitan regions across the country as they continue to become more diverse. We take a long view, assessing trends since 1980. There are two main findings: 1) the slow pace of lowering black-white segregation has continued, but there is now some change in the traditional Ghetto Belt cities of the Northeast and Midwest; and 2) the rapidly growing Hispanic and Asian populations are as segregated today as they were thirty years ago, and their growth is creating more intense ethnic enclaves in many parts of the country.