I know this might be a little late, but here are a few suggestions:
1) BW-3 on Exchange Street just off campus of The University of Akron. They have a projection screen that I'm sure will be showing the game. Approx 10 minute drive from Cuyahoga Falls.
2) Winking Lizard on W. Market St. in Fairlawn (West Akron). When I lived there a few years back, they used to have every NFL game on in the bar on Sundays, so I'm sure they'll be showing OSU. About a 20 minute drive from the Falls.
3) Damon's on Montrose West Ave. in Fairlawn. Multiple big screens. About 20 minutes away.
The thing is that I can't really think of any sports bars at Chapel Hill, which would be much closer to the Falls (they closed the Damon's there a few years ago).
I'd probably go with Winking Lizard, although it is kind of a drive.