my daughters' school is 43% white, 33% hispanic, 10% black, and 4% asian. that's pretty integrated.
northside prep is the best high school in the state, its 31% white, 30% hispanic, 20% asian, and 10% black. that's pretty integrated too. walter payton (the second best high school in the state...yes, its named after a football player where do you think you live?) is 44% white, 21% hispanic, 20% asian, and 10% black.
i live right on the border of albany park and lincoln square. albany park is 45% hispanic, 32% white, 15% asian and 5% black. pretty integrated. lincoln square (much wealthier) is 65% white, 18% hispanic, 9% asian, and 3% black. not so much.
humboldt park is 49% hispanic, 23% white, 23% black, and 1% asian.
englewood, by contrast, is 94% black and 4% hispanic.
the city as a whole is 33% white, 29% black, 28% hispanic, and 6% asian. with the black population shrinking dramatically and the asian population growing quickly.
a few pockets of "diverse" neighborhoods here and there, but you can still divide the city into thirds with blacks to the south, whites to the north, and hispanics to the west. its not universal by any means, but that general split still applies.