One thing to keep in mind, near most national and state parks there will be private campgrounds close by. We have a 38 foot 5th wheel and have always been able to find a place to stay within 25 miles or less of the national or state parks we wanted to visit.
Great thing about private parks is you can get full hook ups which can help make the whole experience more enjoyable. It's bad when the batteries die while you are trying to take a shower with no hook ups. That happened to us in our 25 foot TT at Zion National Park in 1980.