What Chicago neighborhood should we choose?

My husband, four-year old daughter, and I are moving to Chicago and are looking for a place to live. We have to live in the city due to his employment, but we are unsure what neighborhood is the safest and most diverse. We are African-American and prefer a place with diversity. I mentioned our race because we've recently had issues at my daughter's school where some of the other students exclude her because she looks "different" (we live in Indiana- and it's not really progressive here) I would like her to be exposed to all types of people, including some who look like her. What neighborhoods can anyone recommend?

Oh, by the way, we are looking for an apartment and would like to spend around $1500 a month, but can go as high as $2100.

Thanks for the help everyone!