Not sure how far you want to travel.
If you need to stay close by I would second Starved Rock State Park. Also, Shabbona Lake State Park, and Kankakee River State Park.
They're not exactly what I would call remote, but their sites are usually separated by some trees/woods. This is as opposed to the KOA's, Jellystones, etc., where you are right on top of each other with little or no privacy.
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