What do you mean by “current injustices that are derived from these things?” How do you wipe out the legacy of slavery?
As for white kids going to private schools, I am not sure what can be done about that. This is America, if you have enough money amd want to send your kids to private school, you can.
I pretty sure that housing segregation is not allowed under the civil rights act. People have the right to live where they want regardless of skin color, assuming they can afford to live in said place.
I think a few people (CatBus, DominicCobb, and suspiciouscoffee) have already done a good job of responding to this, but I just wanted to throw in my two cents. You ask how racism/segregation is still prevalent in American society, and you have twice answered your own question. If the ability to live in “nice neighbourhoods” and attend “good schools” is contingent on having the money to make such things possible, and if certain races generally don’t have access to such money, then this is a form of racism/segregation.
Now one might argue that anyone, regardless of race, has the opportunity to make enough money to live where they wish and attend whatever school they wish, but if society is set up to keep people in their existing socioeconomic class, and if people in lower socioeconomic classes are generally minorities, therein lies the institutional racism mentioned earlier. If a child lives in a poor neighbourhood and attends a poor school due to his family not having enough money to do otherwise, then the child himself is likely to grow up and find himself in the same boat. The cycle perpetuates itself, not because any one person is saying, “Don’t live here” and “Go to school there,” but simply because society makes it difficult to escape one’s current class, and due to American history, many racial minorities find themselves in the lower class.
For anyone interested in learning more about the culture of poverty, and why it is so difficult to escape it, I’d recommend reading Building Bridges out of Poverty.