Kentucky is a great state to travel in by small RV. There are numerous campgrounds and historic sites to see. Highway 64 generally bisects the state west to east and Interstate 75 generally bisects it north and south.
There's a long list of historic attractions here you can see from a small RV. You can see the birthplace of Abraham Lincoln in Springfield, on your way to the world famous Mammoth Caves from the Bluegrass, the central part of the state around Lexington and the capitol, Frankfort. Consider the Bourbon Trail as this connects all the major bourbon and whiskey distilleries in the area. In Lexington, you can visit the house of Mary Todd Lincoln, Transylvania University where Jefferson Davis attended college before becoming president of the Confederate States of America and Keeneland, where Lexington goes to wager on world class thoroughbred racing. Remember the University of Kentucky Wildcats play in Lexington but they are an extremely popular draw and the arena usually sells out.
In Louisville, you can ride the Belle of Louisville which is a big paddle wheel river boat that is great to ride and see the fireworks over the Fourth of July. The Louisville Slugger Factory and Museum is here where you can get some batting practice in and watch how these great examples of sporting goods craftsmanship are produced. You might even take in some world class horse racing at Churchill Downs where a little race called the Kentucky Derby occurs every year.
If you are into kayaking or like views of water, keep in mind that the state has the longest complex of navigable waterways and streams outside of Alaska. There are lots of campgrounds well suited for a small RV about an hour east of Lexington near the famous Red River Gorge, in the Daniel Boone National Forest, which offers fantastic views and rappelling if you are equipped for that. Guides can offer lessons and equipment in the area. Nearby Natural Bridge is just that: a wind and water eroded natural bridge with a lift nearby for some great photo opportunities.
In the southeastern portion of the state you can find the Cumberland Falls State Park which besides the natural beauty of a pristine waterfall offers the world's only known moon-bow!
Consider this unique state rich in natural attractions and history to visit and there are lots of accommodations for a small RV.