Chicago is pretty segregated as whole. The North side is predominantly Caucasian and the south side (save for a few neighborhoods) is predominantly African-American and Latino.
Sure Chicago is segregated (though I find the North/South boundary, like all generalizations misses a considerable amount of complexity) but this is true of all US cities.
San Francisco for instance is segregated pretty dramatically with the Asian population (and a mixture of Latinos) pushed to the western edge and the white population centrally located. Not to mention the elephant in the room of Oakland.
When we start talking about diversity of other sorts such as income, education, nationality etc the picture is similar.
That is to say, my experience of San Francisco was one of homogeny, the opposite of my experience of Chicago. But I've experienced Chicago more broadly as well, so as I say I'd like some numbers to backup the assertion that San Francisco is more welcoming of inter racial families.
