For the record, you pronounce the ‘s’ in “Des Plaines” but not in “Illinois”. Rivers Casino Des Plaines is the closest Illinois casino to downtown Chicago.
The best options, especially with Indiana expediting legal sports betting, are just over the eastern border of Illinois. There are a smattering of serviceable, albeit unexciting, casinos in the Chicagoland area. Chicago has a ways to go be considered a great gambling destination.