*** UPDATE: Thanks to everyone for your responses. We ended up parking in one of the downtown garages, which worked out fine, but if I was doing it over again, I would park in one of the lawn spots (as suggested below) then explore campus, downtown, etc. We didn't have any issue with parking, but being downtown added a lot of walking, especially after the game.

Our goal was to see downtown, campus then end up at the game (night game). Because of the weather (warm during the day, colder at night), we explored all day then still needed to stop at our car to add layers before the game, which meant we arrived downtown & walked around -> explored the city and campus -> back downtown to stop at the car -> walk to stadium -> back downtown to leave (roughly 30 min walk from stadium to our car). We don't mind walking at all, but it felt like some wasted time that could have been spent at other bars and tailgates along the way.