My entire childhood was defined by the trips we took every other year (by not taking vacation in the in-between years, my Dad could take off the better part of the summer the following). Our RV experiences are like others' with boats. As the years went by, they got bigger. An interesting phenomena with trailers. The bigger they get, the less they sleep, lol. Our old 1969 19' Layton probably slept 8. The bread and butter RV of my childhood years were two Hi-Los (looks like a pop-up, with a hydraulic lift) -- these also slept quite a few. By the time I left, they graduated to a much larger rig, an Avion fifth wheeler. There the trend reversed, as it slept at most 6 (two slide outs and all). They've since retired and become nearly full-time, sun-chasing RVers (rough life with a satellite dish up on the roof), and have moved into a diesel pusher 38' motorhome, and that sucker sleeps 4. I guess the RV bean-counters realize that it's the retirees with the disposable income (and inclination) that purchase those big rigs, and don't need to sleep a family and friends as much, anymore. About the only wind that blows them now is he does volunteer audit work for Christian missions (Wycliffe) around the country, so that gives them some direction.
Anyway, our trip that included the Redwoods (mind you, I'm an easterner, so that was a long trip) was a stand-out. RETURN OF THE JEDI was filmed there (that was the "forest moon of Endor"), and I definitely felt a bit like a hobbit there. Gorgeous. In fact, on that same trip, we also visited Flagstaff, and I remember it snowing there, and this was in the middle of the summer... I'm an avid skier now and have been to Utah, Colorado, and Montana a good bit in the winter time, and the Rockies are one of my favorite parts of the country.
The Dakotas would be interesting -- Custer's Last Stand, Mount Rushmore, etc. You could do two trips to the east. I'd think about the South, first. The East introduces another destination equation outside of natural beauty: history. For the former, you'd want to make it to the Great Smoky Mountains, and the Blue Ridge Mountains, especially in northern North Carolina and in Virginia, are beautiful. But, as to the history part, you could go nuts. There are, of course, some very interesting Civil War battlefields. Andrew Jackson's mansion outside of Nashville, The Hermitage, was preserved as he left it right after he died (unique at the time), so that authentically evokes his personality better than most landmark homes. Thomas Jefferson's Monticello, outside of Charlottesville, is a place I never tire of seeing. It was his life's flashaholic-type passion. Of course, the Kentucky horse farms region is a gorgeous region of the south. The Vanderbilt mansion Biltmore is a wonder, as well.
Headed north, there's of course the Smithsonian museums in Washington. Gettysburg Battlefield is interesting even to folks with zero interest in such things -- a lot of drama and very easy to learn the unfolding of that 3 day battle. The Catskill region of New York has quite a few treasures. John D. Rockefeller's estate Pocantico was opened to the public in very recent years. A little further north, in Hyde Park, is FDR's estate, as well as the Val-Kill cottage Eleanor Roosevelt occupied in later years. About two houses up is another Vanderbilt mansion (Frederick?) that's quite the wonder. The Cooperstown Baseball Hall of Fame is is in this area, as well. Speaking of which, a dearth of wonderment (and lobster) lies in Newport, Rhode Island. "Chateaus" that would today cost $100,000,000 to build were created by the Astors and Vanderbilts as summer homes they would occupy for 6 weeks of the year. It was an age that disappeared after the sinking of the Titanic, the First World War, and the advent of income tax.
Headed back home, it'd be worthwhile to head through Ohio where first you can visit the Air Force Museum in Dayton (Patterson AFB) -- it is the largest (to my knowledge) air museum in the world, large than the Smithsonian Air and Space. Among other things, you'll see the reverse prop, humongous wing-span B-36. The Bock's Car is there -- it's the B29 that dropped the atomic bomb on Nagasaki. I was able to run my hands along the bomb bay windows. About mid-way up the Ohio/Indiana state line is a little Indiana town called Auburn. This is where you'll find the neo-deco, 1920s factory headquarters for the Auburn-Cord-Dusenberg car company. It's now a very well-heeled antique car museum. Walking in, you'll see a row of Dusenbergs (one was owned by Clark Gable, if I recall), and that's just the tip of a multi-story iceberg of priceless automobiles, including old Ferraris, a 1919 Lincoln limousine, a Tucker, numerous boat-tail Cords, you name it. Part of the wonder is being in this old-time factory/showroom.
I'm sure there are a ton of things I'll think of later, but these are some of the must-sees that immediately came to mind.