I would suggest looking at a Trailer Life Campground Directory. The front section of maps will have one for Illinois. The dots on the map will tell you whether there are any campgrounds listed for the area in which you are interested and the name of the town. Then go to the Illinois section of the directory and look under the name of the town to find what campgrounds are nearby. Each entry will tell you when they operate if they are limited. For example, some are only open from April 15 - October 15, so they are not open in the winter. This, at least, will help you eliminate some. Elsewhere in the entry will be most of the other information you need such as type of hookups, whether there is a dump station, length of sites, whether there is a maximum length of stay (some public parks have two week limits, for example), and other amenties such as wifi.
Also, if you're near an Illinois Visitor Center (usually on interstates near state lines) they often have brochures about campgrounds that are not listed in any of the large directories because smaller campgrounds especially can't afford the advertisement cost. The Trailer Life and Woodalls directories charge the campgrounds for their entries.
ArdraF