Steubenville had great pepperoni rolls last time I got actual food at a game there.
I can't think of any Ohio specific ones not already mentioned. But nationally, here's a few I remember:Buffalo, Wyoming and Lincoln County, Kentucky both had Ribeye sandwiches.
Springfield, Colorado had chicken wings, 4 for $2. Think I had $10 worth.
Kaycee, Wyoming had Tamales.
Albuquerque, New Mexico at the old Milne Stadium had burritos.
Burgettstown, Pennsylvania had Apple Dumplings (and Haluski and ponczki as well)
A surprising number of places had chili, especially later in the season.
Delta High School in Muncie, Indiana might be the best, though. Complete buffet set up by the boosters for free in the parking lot right next to the stadium. Burgers, brats, and hot dogs, potato salad, macaroni and cheese, pasta salad, rice crispy treats, cookies, and drinks.