As far as the private schools, I think Science & Arts Academy does a good job trying to meet the needs of all levels of giftedness.
http://www.scienceandartsacademy.org/

If you are interested in the Chicago Public School magnet system, this site is very helpful as it walks you through the process, lets you view on a map the school locations, and provides open house dates so you can visit:
http://cpsmagnet.org/apps/pages/index.jsp?uREC_ID=72695&type=d&termREC_ID=&pREC_ID=151352

Best of luck to all parents who are looking for that "right fit" for your family. It can be brutal at times, and I know that it's something most families of gifted have to revisit on a regular basis.

Leslie