ATL,
I wasn't much of the tailgate type of person while I was in school but I can recommend a few fun places to check out. Before you start the tailgate experience, head over to the student union to check out a huge part of campus where most of the student spend their time. Lots of great place within the union to take pictures including the iconic buckeye statue with his leg crossed. If you wanna get blown away by what is the best part of campus check out the Oval. You might wanna bring a ball/freebie or something type of outdoors game to play. This is the single most unifying thing on campus that students walk across everyday as each path guides you to a different place.
I'm not sure if you're the type that likes to exercise before the game but there is a nice running path along the Olentangy river that runs through campus.
Lastly, I recommend you take something home that has Ohio State on it. I've started a shot glass collection of all the schools (tennessee, purdue, wisconsin, iowa, minnesota and ohio state) I've been to and have something to remember each trip.
BTW sorry for whatever construction you may see while you're there. The schools is always working on some project and I'm hoping that doesn't demote your opinion about the campus.