You can find Ohio State Parks and Hocking Hills camping and cabin rentals here for your specific dates: https://reserveohio.com/OhioCampWeb/Default.aspx You can also check https://thehockinghills.org/ for private reservations.
In the Fall, it is always best to book well ahead because lots of people want to come to enjoy the Fall colors
it depends on the campground, I always call before and go ahead and book my rental
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