They run two shuttle bus routes on gameday to the two hotel clusters on I-70, one on the East side and one on the West. Not sure about leaving your vehicle parked at a hotel if you aren't staying there, but there are some restaurants and other places near enough the stops that I would imagine you can work around that.
The campus is nothing special, but the best parts of it are not close to the stadium. There is a big VA hospital across the street from the stadium that is ugly as sin. The main campus, north of there, is not bad, but with it being a morning game, you may not have a reason to go check that out pre-game. As you would expect, they have places to eat and bars in their main campus neighborhood on the north, but that's a pretty good hike to the stadium.
Last time I went there (baseball in the spring), I enjoyed some Italian food at Endwell Taverna.
Shakespeare's is the traditional campus pizza joint located in this neighborhood, but they also have a location in the south part of town.
ETA: It's just over a mile to walk from the off campus bar/restaurant district to the stadium. There are some parking garages in that area that you may be able to reserve, if you don't mind the walk.
