You can count me as another Buckeye that could give some advice to traveling Huskers.
ATL,
A great safe place to take your daughter prior to the game is to Skull Session, which is a pep rally/final warm up for the OSU Marching Band prior to the game. Admission is free and Skull Session starts a little more that two hours prior to kickoff, but you have to get there early to get good seats. The Buckeye team also makes a brief appearance at Skull Session on their way to the stadium. I'd suggest getting there by about 5:00 if you want good seats. If your daughter is in her High School
Buckeye fans have developed a bad reputation as hosts for visiting fans, but that all really peaked in 2002. The atmosphere for visiting fans has really improved a lot in the last decade, and I have heard a lot of positive reviews from visiting fans in recent years. That said, particularly for a night game, there are still drunks to avoid.
I would advise staying away from High Street and Lane Avenue as it gets closer to game time. High Street is the main North-South Street on the east side of campus with lots of shops, restaurants, and bars, and off campus student housing just beyond. Lane Avenue, has several open-air gated, parties/bashes with lots of alcohol available. You can check these areas out in the early afternoon, but the closer it gets to game time, the more obnoxious drunks you will find.
If your looking for a tailgate, I'd suggest west of campus on the west side of the river. This is also the furthest from most student housing, minimizing the number of drunken frat-guy types. Since 2002 the cops have been cracking down and enforcing Ohio's open container laws, so if you choose to consume at OSU, the red solo cup truly is your friend.
I hope you enjoy your trip, and I'm sure it will be great crossing the Shoe off of your bucket list. I think you'll find it to be one of the best College Football Cathedrals in the country.