I live halfway between Chicago and St. Louis along the Illinois River. If you are going to drive from Chicago to St. Louis, then your best opportunity for birding will be to drive down the Illinois River from Chicago to St. Louis. There are many federal, state and local parks, refuges and boat ramps along the Illinois River and in the hills surrounding the river valley with many places to stop and do some birding, to many to mention them all.
Starved Rock State Park, which is right along the river, is one of the most beautiful parks in Illinois and it has many tall, skinny waterfalls. A lot of people drive 90 minutes from Chicago to visit this park. Due to the large number of visitors, this would probably be the best park to get good views of upland birds that are used to being around humans.
There is a backwater marsh of the Illinois River called Dixon Waterfowl Refuge at Hennepin & Hopper Lakes. At this place there is a 30 foot tall birding platform that overlooks the marsh. In and around the city of Peoria, there are many places to see waterfowl along the river and upland birds in the hills. Just outside of Peoria there is a 2,000 acre zoological park called Wildlife Prairie Park. At this zoological park they specialize in only having animals that are native to the Midwestern United States. There would also be good opportunities to see wild, upland birds here, because the animals are kept in fenced in spots in natural, forested areas.
Mendenhall Park and Public Boat Launch is a great place to park and walk along the riverbank and see Bald Eagles if the river isn't at a high level. At Banner Marsh State Park there are dirt roads crisscrossing lakes and marshes along the river with good opportunities to see many types of birds. There is a huge backwater lake along the river at a place called Emiquon Preserve. At different times of the year there will be countless thousands and thousands of different species of waterfowl during migration periods.
Driving down the Illinois River Valley from Chicago to St. Louis is a lot more scenic, than taking the main travel route down Interstate 55. Along Interstate 55 it is just endless, wide open, corn and soybean fields for the whole way. All of the federal, state and local parks, refuges and boat ramps are free to enter. The only place that would cost money would be the zoological park and that is $10 per person with no parking fee.