The Grand Illinois Trail Ride Season is typically September - October when the mosquitoes have diminished, and the nights are longer.
Take 10 or 12 days going 50 miles a day so you can really enjoy yourself. It's a self directed ride on all kinds of terrain: Road, Chipped Limestone, even ballast rock for maybe a total of 5 miles....
A road tire wouldn't be so good, but a thinner mountain bike tire would be just fine.