Last summer we traveled up to Kansas City, KS for a meeting, then planned on stopping at several Presidential Libraries - it was raining and unable to stop, Elkhart, IN has a lot of museums in Elkhart and nearby. I use an electric mobility scooter and Mother Nature decided I couldn't go sightseeing.
Pontiac, IL has free parking downtown and has 4 museums that are free - donations gladly accepted. One of the museums is about Route 66. They have markers so you can park near the courthouse, and walk to all the museums. They had some fiberglass vehicles that had been painted with the Route 66 theme.
Auburn, IN has several car museums and an aviation museum.
If we had had time and more money, we wanted to go into Michigan to the Gerald Ford museum - the stairway from the American Embassy in Vietnam is there. And Detroit has several museums.
The only thing I could suggest is write or call the different state visitor bureaus and get their information ahead of time to find things you are interested in. My husband likes military museums, especially aviation and we both love old cars. When we were in Wisconsin in 2007 (with a car only) we visited several museums in northern Iowa and Illinois. In Kentucky is the Corvette museum (if not Kentucky, then Tennessee). There are a lot of Civil War sites all over that area. Bardstown, KY has a museum and a 'town' next to it and also museum about whiskey, tours of a couple distilleries and "My old Kentucky home".
For Texas, call 800-8888-TEX.
Arkansas has Clinton Library, north of Little Rock is a state park and a car museum. Just plan on driving about 250 miles per day so you don't get too tired and can get to camp early. Plan on stopping at some of the little sites that a small town is proud of - the locals can help you find other things too.
Also, look to see how far someplace is from home to travel on a Friday, stay until Sunday afternoon for mini vacations. What is 200 miles from home? Festivals? county or state fairs? etc. and explore you own state. Plan once a month to do a mini-vacation or stay-cation. It will give you something to look forward to and learn more about your RV. This way, you can go to some areas of your state for produce and have a way to bring some home. At least, with your home with you, you can save on restaurant meals and hotels.