Your recommendation is the best for opposing fans. Myrtle is awesome and offers a perfect experience. Pardon me while I post my other suggestions again:
You want to be downtown on the Ped Mall. The Iowa Beer Band usually begins their tour after 8pm and stops at Brother's, Sport's Column, Joe's, and a few bars I'm forgetting. Simply, the members of the marching band that can drink play a few songs in bars the night before the game...it's fun.
Food recs- Joseph's (if you want a steak and upscale experience), Green Orchard (upscale), Pullman Diner (intimate, hand-crafted menu), Vue Rooftop (great menu, make a reservation), Mickey's (great bar food and environment), Saint Birch Tavern, and finally grilled cheese from Marco's food stand.
Bars- Joe's Place (upperclassman, professors, locals...GO HERE!), Airliner (staple in Iowa City since 1920s), Brother's (younger crowd), Sport's Column (my favorite undergrad bar), Deadwood (legendary hipster bar to show IC's quirkiness), Clinton Street Social Club (craft cocktails, nice view of Old Capital).
I'm hosting many Gopher fans this weekend. Rightfully so, my Minnesota friends are coming out of the woodwork for this game. Enjoy Iowa City!