Jim, I live about 50 miles south of Romulus and if you can check out the race schedule at the Watkins Glen track, it may mean a place is open in Watkins Glen NY during that time of there is no race. There's a KOA there which I dislike, but it's there. Watkins is about 25-30 miles south.
I stay in a fairgrounds in Horseheads NY about 18 miles south of Watkins. Always a space there. It seems that The KOA in Canandaguia is much further.
I do not know the availability of campgrounds north of Romulus.
Here's a thought. Sampson Air Force Base (closed, i think ) has a campground and is a few miles from Romulus. I think it is a state campground if you're looking for the listing.
Good luck
Lew