Moving to Chicago, looking for top public high schools

Northside Prep, Whitney Young, Lane Tech, and Payton are some of the top high schools in Chicago! Depends on which side of town you live on & how far you want your child commuting.

Are you limiting yourself to the city proper or are you also including suburbs? If so,how far out?

The City of Chicago is huge, and if you include the close-by suburban communities, as well, then you've got a multitude of options.
My nephew and nieces attended CPS Magnet Schools. Currently the girls are at Whitney Young High, and the boy has graduated and is now in college....he amassed countless hours of AP credits, and received numerous all-expense paid college scholarship offers.
Within the City of Chicago, I would definitely recommend Magnet schools over neighborhood schools if your child is bright and motivated, although I'm not sure how the enrollment process would work for someone who is just moving into the area now, since testing/applications are typically done in spring for the following fall school year....