I have lived here for 13 years. Manny's on Second (upper east side) is the defacto Buckeye bar. You'll still hear some refer to it as Blondies. A little history...Blondies upper west was THE Ohio State bar for many years, then they opened Blondies upper east which became THE Ohio State bar. Something happened about 6-7 years ago and Blondies upper east became Manny's on Second. The official Alumni club has since left for a bigger venue, but it's a great crowd and you avoid the Times Sq scene.
I strongly recommend venturing out of Soho to watch the game. The Soho crowd is not a big football crowd and you won't find a bar with the sound of the game outside of Manny's or Iron Bar. The food at Manny's is very good for just bar food. Waffle fries, burgers, wings, all good and consistent.
Let me know if you need any more recommendations.