I suggest an alternative source for maps of bike routes in the Chicago area: the Chicago Bicycle Federation (
www.chibikefed.org) sells a map that shows recommended routes throughout the metro area. Its recommendations are based on data gathered from actual riders, whereas the State Department of Transportation relies on some other system that I've found to be pretty unreliable. I used to live in South Downers Grove, and the roads the State map recommends are absolutely nuts.
I don't know which South suburb you live in, but there is a paved rails-to-trail that runs east-west just south of Highway 30 from Park Forest to New Lenox. In the Mokena area, you can turn south and find some nice rural two-lane roads for rides. The web site for the trail is
www.oprt.org.
There is a great recreational riding club in the South suburbs named the "Bike Psychos" (
www.bikepsychos.org). They are based on Oak Lawn. They sponsor a terrific century in late August in Coal City, about 20 miles south of Joliet.