On a more serious note, my kids attend(ed) extremely diverse nyc schools and they were excellent in their own ways. In NYC it might be worth noting that quality is not determined by the color or ethnicity of the student body as it often is assumed and as it may be elsewhere.
In one HS my child’s ethnic identity group made up just 7% of the population and the poverty rate was above 2/3 of the student body. So technically it was segregated by the larger ethnic groups that made up 93% of the student body. It was also one of the most innovative schools in NYC, a city with lots and lots of innovative schools. This HS has a hands-on program that if I described it, it would be hard to believe, in terms of programming, the lovely location, and the out-of-school activities. Gorgeous facilities overlooking the Statue of LIberty amid ground designated as part of the National Park System. My uber nerdy child had all of this space to run around and, not one for athletics, learned to parkour.
Middle school–also one of the more ethnically diverse schools and one of the top middle schools. Very innovative, progressive programming.
In fact: it might be interesting to note that some of the top, highest-performing high schools also have some of the highest concentrations of first-gen kids with various skin tones and who speak a language other than English at home.
The bad thing about choice in NYC is that some people seek out “their own.” On the flip side, if you live in a homeless shelter, and you can figure out transportation, you CAN get your kids into a fabulous school. This happened in our grade school. A family living in a shelter in the Bronx, single dad, working, with kids, he got his kids to school in Manhattan every day. A really good grade school. And probably gave them a better economic boost in life as a result.