The Antique Car Museum of Iowa is a specialist stop near Iowa City, focused on vintage automobiles, signs, petroliana, and the material culture of early motoring. It is not a broad city-history museum, but the collection has enough personality for travellers who enjoy mechanical nostalgia.
It is best treated as a selective add-on, especially if you are already around Coralville or travelling with someone who likes historic cars. For a first Iowa City visit, the university museums and literary sites matter more, but this fills a different niche well.