Michigan is beautiful state that is easily accessed from Chicago. You can drive the toll road through Indiana and be in South Haven in just a few hours. Or you could drive a little farther to Muskegon or Holland and start to hit the forests regions of western Michigan. Lots of camping and great beaches formed by the dunes. The Upper Peninsula is a long drive north from Illinois but I've heard it's awesome up there along the shores of Lake Superior.
Following are links to many of the places we have visited along with camping and general tourism sites.
Mike's Virtual Vacation Web Page - www.geocities.com/mike_knott/michigan.htm
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