We did a smaller version of what you are going to do back in 2002. Mt Rushmore was the farthest we got from home. We took a chance and booked nothing. I’m not suggesting that, just sharing. We used Good Sam info, maps, and we had this huge book, that has every interstate exchange in America, and what was available at each. Obviously, this was before google on phones. A lot has changed technology wise. We were on a tight tight budget, and did it fairly cheap. 5700 miles, 2300 bucks, for 23 days, not including a mechanical repair of 600 bucks in Denver. As I said, times and economy were different. Gas was 1.15, most sites were 25 or less, ate out very little as well. The only time we had a problem camping was at the very end of the trip, we wanted an extra night or 2, but it was July 4, and there was nothing between gatlinburg, and north Florida, so we booked it home, 12 hour day. Keep holidays in mind like that. The wife would thumb through the books on the road, and find campgrounds to call while traveling. We were going to stay in a state park in Wyoming, but poor planning on our part, we didn’t fill the water tank in the camper, so we found another spot, late in the day. It worked out. We would have stayed at the SP with no power, but no water, we decided not to.