We've done several road trips in the US. The South West National Parks are great - (Grand Canyon, Bryce, Mesa Verde, Zion, Arches, Monument Valley), but in Summer unless you are high up it is very hot. Its easy to get carried away with a list of "must sees" which mean you drive too much and don't spend enough time anywhere, we are very bad at this. The low humidity makes the heat more bearable and everything is air conditioned. We usually combine camping in a tent and staying in motels, the motor home thing has never appealed to me, they are expensive to hire and you are stuck with driving around in a huge vehicle all the time unless you tow a car which is what a lot of Americans do.
Yellowstone is amazing, lots to see and do, we have been twice and still haven't seen it all. It is also cooler there (I hate heat). You need to be aware that accommodation, including campsites, in the park books up very quickly and it is large so staying outside does sometimes mean a long drive to get to the sights.
My favourite was Seattle and Washington state, much less crowded, we went to the North Cascades National park which is remote and beautiful and full of huge trees, a fantastic experience (and the polar opposite of Las Vegas which we hated). We also went out onto the islands to Olympic National Park and some of the little towns, including Forks which is now famous for one of those vampire series and therefore may not be as unspoiled as when we went there. You can easily combine Seattle with Vancouver as well. Both are nice cities to spend time in, particularly Seattle.
Next I would like to do New England...