You state you'll probably be west of the Mississippi. O.K. problem solved.
As I stated above, we have had absolutely no problems finding sites with our 40' motorhome mostly west of the Mississippi.
One comment above was about Yosemite. That is one we would not try. In fact, California is a different 'breed' entirely for their state parks. However, in California there are wonderful county parks that compare favorably and sometimes even better than their state parks. We have also stayed in great forest service campgrounds in California. So....don't limit yourself to state parks. There are other options. For Yosemite, we stayed in a forest service campground between Lee Vining on 395 and Yosemite. We are also member of the Escapees RV Club and they have a park near Yosemite where we have stayed. Regardless, Yosemite is not a favorite park of ours - too many people period.
Regarding national parks, we have stayed multiple times in Yellowstone, Grand Teton, Glacier, Zion, Bryce, Canyonlands, Grand Canyon and others. In fact, some of our visits have been without even having reservations.
We have stayed in every state park in Arizona and many others in New Mexico, Colorado, Utah, Montana, Oregon, Washington and more.
There is absolutely no problems finding spots with a big rig - especially in the West.