You're talking about the Carver College of Medicine right? If so, I stayed at the Motel 6 a few miles away. It was crappy but cheap and there was free HBO so I couldn't complain too much. But that whole street is filled with inns/motels so you can't go wrong.
Most of the hotels around the school give a 'hospital rate' if you're interviewing, you should ask. Also, I stayed at the Iowa House, which is actually a hotel on campus. Its in the U of Iowa Memorial Union, and they have a shuttle that will take you to the campus in the morning and if you call them, will bring you back to the hotel in the afternoon. The posted rate for the place is about $100/night, but if you get the hospital discount, it should be only about $50.
Also, something that you should consider, when you get to the Cedar Rapids airport, you'll want to either get a taxi or go to the shuttle window and book a shuttle for the ride to the hotel and the ride back to the airport. Its about $50 but its pretty much the only shuttle service (the hotel doesn't take you to the airport).
PM me if you need anything else! Happy interviewing! 👍