Have you checked out the Illinois Bicycling Maps? The IDOT website has them in downloadable form, or you can get them for free from IDOT.
I wouldn't rely on Google Maps. Use the Illinois Bicycling Maps instead.
Illinois is a great state to cycle in. There are tons of lightly traveled roads with decent surfaces. Here's a journal (8 pages) of a trip I took with my son in downstate Illinois earlier this year from Carlinville to Princeton (the link here is to the table of contents): http://www.crazyguyonabike.com/doc/?o=1&doc_id=10337&v=7j
I'd suggest going WSW from your home, maybe cutting south in the Princeton or Kewanee area. You could use parts of our route from Princeton to Carlinville, and then cross the Mississippi River at Alton. There is an entry on Crazyguyonabike that gives the way from Alton to the Katy Trail's beginning at Machens, MO. Then you take the Katy Trail to Columbia.
Here is the link to the Alton to Machens route: http://www.crazyguyonabike.com/doc/page/?o=1&page_id=264286&v=9o&part=2
As you can see from my journal, the crossing of the Illinois River in Peoria wasn't bad at all, and the Peoria metro area was pretty easy to get through because there are quiet streets and rail trails for much of the way. Here is the page which has a detailed map of the route through Peoria (scroll down toward the bottom of the page), you can enlarge the detail: http://www.crazyguyonabike.com/doc/page/?o=1&page_id=276550&v=3u
Almost all of the roads we traveled on were great bicycling roads. The road from Illinois 104 to New Berlin, IL had heavier traffic than most, but we stuck on it because we had a great tailwind and a good surface and were just clipping along. There are paralleling roads that would be lighter traffic. And of course there is more traffic south of Peoria and in Peoria, but again, there was a good shoulder for the most part on the more heavy roads. If you have specific questions about specific roads, let me know.