I've been to several Iowa games over the years, including a couple of non-Gopher games. I would try to do the public parking at the
Finkbine Commuter Lot #65 (across from their basketball arena). Don't confuse it with the actual Finkbine Golf Course parking, which is a different road altogether (and also an option, but if its raining they won't let you park on the course).
I like the commuter lot because it is hard surface and a little closer to the stadium and I think a better tailgating situation. It is open to the public for $25 per car, but you have to get there well ahead of kickoff (like 4 hours ahead, which if you want to tailgate, go for it). Depending on where you bought your tickets, you can buy a prepaid pass for that lot. If you have a car full of people, it'll be cheaper than taking the train at $12 per person, too. Plus if you take the train, you really can't tailgate on your own since you park at the Mall. You would need to go find people to hang out with.
https://footballgameday.hawkeyesports.com/public-parking-2