Maribeth,
Your goal in visiting and photographing our county courthouses sounds great, we will follow your progress with great interest. We have visited many of our state parks and almost always find them peaceful and well-kept. During September they will be busy on weekends but reasonably empty during the week. Some of our favorites are Red Haw (Chariton), Pikes Peak (McGregor), Springbrook (Bagley), Back Bone (Strawberry Point), Waubonsie (Hamburg), etc. The COE parks at Rathbun, Red Rock and Saylorville are very nice.
Many of our counties have set aside "county park" areas some which have campgrounds. You can get an online guide to these areas @ www.mycountyparks.com. I think they may even print a hard copy directory of these areas.
September is a beautiful month in Iowa. Have a great trip.
Welcome to our state. Send me a PM if I can be of any help.