I think North Augusta to Nashville to Hannibal would work nicely and leave you only about 150 miles to Iowa City on Day 3. However, if you want to avoid the hassle of Nashville, you might press on to Clarksville, TN which is only about 40 miles further. There are a number of motels right at Exit 4.

Hannibal is something of a tourist town and you might find rates would be cheaper during the week than on a weekend.