I wrote the Illinois DOT and received a packet of the 8 bike maps. They're good. The roads we took on a recent trip based on those maps were nice and quiet (link is to an 8 page journal with pictures of some of the quiet roads, as well as using Metra and Amtrak with our bikes): http://www.crazyguyonabike.com/doc/?o=1&doc_id=10337&v=7l
All roads colored green on the bike maps are good in my experience, the yellows are fine too for the most part as well. Even some of the so-called less desirable roads can be just fine as well.
The bike maps from Illinois are a much better resource than Google for this purpose. Print out the counties you want and use them to map a route.
So, consider riding north from the Northern Tier on quiet county and town roads (using the bike maps) to University Park (which is the southern terminal of the Metra Electric line), catching a Metra Electric commuter train to downtown Chicago, then transferring to a Metra train to Palatine. If you do it on the weekend, the fare for both trips is only $7.00. Keep in mind that there are some blackout dates and times for bikes, typically rush hours peak directions and certain events (check the Metra website for details)