IMSA is a public boarding school, widely recognized as among the best schools in the country, public or private. Admission is competitive for top-scoring Illinois residents, and is mainly based on standardized test scores and teacher referral. You have to have excelled in math and science to have a chance, but once you get in IMSA has good performing arts and humanities programs as well. Its college admissions profile is excellent, on par with schools like Stuyvesant.
Keep in mind that it does differ from some more traditional East Coast boarding schools in that many students from the Chicago area leave on the weekends, so dorm life may not be as emphasized.
My brother and sister both went to IMSA; feel free to PM me if you're admitted.