Since you will be hitting St. Augustine and Savannah early in your trip, a couple of suggestions up front,
Stay at a campground outside St. Augustine and take the trolly in the city. The streets are too narrow for comfort with your tow vehicle and parking is scarce. Do spend some time in St. Augustine if you haven't already though, as it is a great town to see.
While you are staying near Savannah, don't miss the Mighty Eighth Air Force Museum Home @ the Mighty Eighth
. It is one of the best museums of WW II that I have visited--and I'm a museum buff.
Someone suggested seeing the Bicycle Museum in New Bremen, OH while you are staying near Jackson Center. I definitely agree! Bicycle Museum of America
While you are staying near Jackson Center you might want to head about 50 miles south to see the National Museum of the United States Air Force, which I believe is Ohio's number one tourist attraction. National Museum of the USAF - Home
If you're into aviation, you could easily spend a whole day there.