The intelligentisa cup in the summer at the end of July is great. A 10 day road/crit omnium race. http://intelligentsiacup.com/
For cyclocross check out https://chicrosscup.com/ 100+ entries in the Cat 4/5 are typical during the early races in the series.
Just north of the border around Milwaukee is https://www.tourofamericasdairyland.com/
11 straight days of crit racing.
20 miles southwest of the city there are great MTB trails near Palos Hills. Mountain Bike Trails near Palos Trail System