From campus, student housing is to the east of High Street and north of Lane Avenue.
Walking through these areas could result in heckling at a minimum and possibly worse if anyone in your party engages… however, this being a noon game drops the risk down pretty substantially.
(Edit: Important note, you almost certainly want to avoid walking through student housing after the game if you can… I’d walk straight west on Lane and try to catch a ride near the Schott if you’re staying at Polaris or Easton, and just walk south on High Street until you can get a ride or just get there if you’re staying in the Short North.)
There are tailgate lots right outside the stadium, and to the west by Jesse Owens Stadium (and other places mostly to the west of the stadium). You shouldn’t run into any issues finding friendly groups as long as you’re not an asshole.
The Short North and the Arena District (which are adjacent to each other) are the trendy places in town to stay, eat, and go to bars. Almost everything is walkable or a short ride from there, with campus being a few miles to the north.
If you’re interested in staying further away, which is probably cheaper but I don’t really know because I’ve never had to stay in a hotel in Columbus, look at the Polaris or Easton areas. There are plenty of hotel, dining, and entertainment options in these areas as well. Easton is kinda walkable (the setup is like a big outdoor mall), the Polaris area is not at all walkable.
The ride to campus will obviously be more expensive from these places, which are near the outer belt, than from the Short North/Arena District.