Lakes - probably the only city in Ohio that isn't overwhelmingly Ohio State is Cincinnati. And there are a lot of Buckeye fans there as well.
Youngstown, Kent, Akron doesn't matter - OSU comes first with most people. its part of the challenges of selling tickets. The local school is the #2 school in most of the state and people would rather stay home and watch the Buckeres on TV. You will see a lot more Ohio State garb this weekend outside of the game. People love a winner at the highest level - and that's tO$U.
As Pita said, enjoy your visit, spend lots of money, travel safe but go home unhappy with the result.