The short answer is -- you can't. If you live in the city, and you don't send your kids to CPS, they will attend a private school.
The long answer, though, may be of more interest to you. There are many options within CPS that are attractive and worthwhile. Among them are charter schools and selective-enrollment programs.
Go to the CPS web site and take a look at the School Locator:
Click "Search by Address," then enter an address in the neighborhood you'd like to live. Make sure to select a search radius, the wider the better.
Next, make sure to select only "Level 1" schools under "Performance Rating." Click "Search." The map results, which are clickable, will show you only the highest-performing schools in the search radius.
You can then select one of the pins to view information specific to the school. This information will include whether the school has selective enrollment or is a neighborhood school and its attendance boundaries.
CPS has many fine schools, you just need to do your homework to find them. The top high school in Illinois, Northside College Prep, is a Chicago Public School. Many of the top elementary schools are also within the CPS system.
Successful public schools generally are those that engage parents and students alike. If you do your homework, I'm sure you'll find one you like within the city limits.
Don Pasek, CIPS, TRC, ADPR
Omniterra Real Properties
Options you have for your kids are:
If that is not satisfactory, and you really need Chicago residency then obtain 2 properties:
one in Chicago for your residency and one elsewhere in an area where you like the public schools.
If you are in Chicago, then you are in the CPS district. There are many highly rated public schools in the city of Chicago. Are you relocating to Chicago? I would be happy to talk with you and find a home and school that meets your needs.