As others have said, your license is honored in every state, just as if you were driving a car. If you're legal to drive your RV in your home state, you can drive it anywhere in the country.
There is no state that requires a CDL to drive a personal RV for noncommercial uses. Some states do require different classes of driver's licenses for their residents, and often these classes parallel the CDL classes, but such licenses are not commercial driver's licenses and do not have the same requirements for logging hours and submitting to drug tests and getting approved physicals and so on.
