Since you listed this under “private high schools”, there is the Chicago Academy for the Arts which draws students from the suburbs as well as the city. And many high schools can have robust music, drama and visual arts programs, along with strengths all across a curriculum. Look into visiting or shadowing schools to see about their arts offerings.

For public schools, definitely check out programs like Senn, Lincoln Park and Curie fine & performing arts for their audition or portfolio based admissions options.