There are some new websites where RV owners list their RVs for rent. The prices seem to be cheaper than the nationwide rental companies. Do a Google search and you'll see the new websites...one is outdoorsy.com.
If you already had the RV and it is dependable it would be the least expensive way to travel. Buying an RV or renting will drive your costs up to the same as a plane or car trip and stay in hotels.
Another thing to consider is many of the RV parks, campgrounds and even some state and national parks offer onsite RVs or cabins (small mobile homes/ tiny houses) to rent. So you would travel from destination to destination in a car and spend the night in one of these accommodations.
There are also companies and private owners that will park an RV at a site for you to rent.
Good luck in your decision and have a great trip.