At this time (August 15, 2005) there are practically no hotels near the fairgrounds. Moreover, there is no city wide bus service on Sundays which would connect you to the route that would take you to the fairgrounds, although there is a shuttle service from such destinations as the state house and a parking ramp on the north side of downtown Des Moines.
Be prepared to walk and walk and walk. They have tractors which pull trams around the fairgrounds, but you need a copy of the schedule to find out where and when they run. Moreover, part of the fairgrounds are located on a hill. You might want to take the chairlift--which costs a small fee. The chairlift takes you from Ye Olde Mill (similar to a tunnel-of-love) uphill to the cultural center.