Yes, the interior is eye-catching. It looks very comfy and welcoming.
The I-80 corridor should be reasonably cool at night. I-40 could be blistering hot in many locales, though. I like to use a website like wunderground.com or weather.com to plug in cities along my route and see what their forecasts and the typical highs/lows are for the time period. I think about how far I intend to travel (roughly) each day and then I locate a few possible campgrounds in each of those areas. If it's likely to be uncomfortably hot I map out the CGs in the higher elevations wherever possible.
For example, on the route back you could spend a night around Mammoth Lakes, where there are many campgrounds but also tons of boondock sites under the trees on national forest land. I spent 2 nights boondocking
at Sagehen Meadow, a bit east of Mono Lake and just 2 miles off the main highway, yet I saw not another soul the whole time there.
From there, I would drive through about 500 miles of hot dry country to get to the mountains east of Cedar City, UT. There you have Cedar Breaks National Monument at over 10k feet and Panguitch Lake at about 8000', with many sights like Zion and Bryce Canyon nearby. Also it is not far to the north rim of Grand Canyon, which is also 8000'. The park CG is usually booked, they say, but there's boondocking
on NF land just outside the park boundary (some folks drive the forest roads east and then SE until they hit the Canyon rim itself, and camp there!) as well as a NF CG at Jacob Lake.
From there, a day's drive through more hot desert would get me to northern New Mexico. I would take US 64 into the San Juans. One time I boondocked along a forest road just a hundred yards off the highway, at 9000' elevation; east past Tierra Amarilla the highway climbs to a high pass and then begins to go back down, and about 2 miles later the forest road headed north. But that wasn't the only one; there were other dirt roads here and there as well. Very quiet and peaceful with little highway noise. The view of the valley coming down into Tres Piedras was fantastically green and beautiful. Another place I've stayed at is Hyde State Park just east of Santa Fe; you climb sharply out of town to over 8000' and there's both the state park and a national forest campground up there. A short hiking trail climbs from the campground to the top of a ridge, where one can look down upon Santa Fe far below.
Unfortunately, once past NM there are no mountains to speak of from there to TN. But one area worth camping at is central Arkansas, at either Mount Magazine SP or Petit Jean SP. I've been to the latter 3 times and it is one of my favorites. High overlooks (drive or hike), a couple of waterfalls, interesting rock formations at Bear Cave and the Turtle Rocks, and plenty of nice trails. These parks are only a few hundred feet higher than the surrounding area, but every little bit helps at night.
As for reservations, I rarely make any because I want maximum flexibility. I always have a couple of nearby backup places figured out in case my first choice is full. But some people find reservations comforting. You could always call a place 1 or 2 days before you'll be there and book a site, and still retain a lot of flexibility in your trip. I don't even know how some folks book out and reserve their whole trip... and then they have no choice but to race to the next destination even when when they hit bad weather or they find some area they wish they had more time for.
Are you going to hit Yosemite? I was there last year. That place books up 6 months in advance! But I can tell you how to get a campsite in the park on the spur of the moment.