As I said, I don’t know of any. Fairgrounds are usually owned by a fair board, which is generally a nonprofit corporation.
But, if there are some where the land itself is ultimately publicly-owned, I bet even they are leased for the duration of a fair to such a nonprofit group, which would mean it would still be handled like private property for the purposes of dictating who and who could not do what on the property.
Again, I don’t know of a single fair that you could go to and do anything you want.