Public parks are always our first choice and we stayed in them 95% of our 16 years of full-timing. We also volunteered in them.
Our 40' fit in Yellowstone, Grand Teton, Glacier, Zion, Bryce and many more. We've also stayed in hundreds of national forest campgrounds along with Corp of Engineers, state parks, county parks and city parks. We also boondocked in off the highway places and spent the summer in Alaska, staying at those kinds of places.
We love driving mountain roads and there's a publication called 'Mountain Directory for Truckers and RVers' that I would recommend.
When folks say you can't do it, they either have not tried or it's not their kind of RVing. I will say that you have to do more research for places but we've never been turned away because we couldn't fit.
Have fun in your new lifestyle!