Keep in mind, and I don't know exactly when, but things start shutting down in Yellowstone and Grand Teton about mid Sept; just do your checking out. We were there last year about 2nd week in Sept and it was beautiful.
That's true, another complication, huh? Some campgrounds and facilities begin to shut down then, but others will remain open. You could conform the details online or with a phone call. Another thought, weather at high elevations is unpredictable so I think it would be wise to take at least one set of cold weather gear in case you get caught in a freak winter storm. I've been snowed on there in the dead of summer.
Also, since you delayed your trip a couple of weeks the parks in southern Utah will be more palatable. The closer to October the better. The exception is Bryce at 8000', it's cool even in the summer. You'll also be within range of the Grand canyon there. I prefer the north rim because it's much less developed, but for first timers I'd recommend going to the south rim. It's about another 200 mile drive from the north rim.
Here's a site for Yellowstone campgrounds which gives the closing dates. Note that the campgrounds without an asterisk don't accept reservations so there's always room at non-reservable ones if you get there around 10am. We've done it many times.
Yellowstone and Tetons are a must as several have mentioned. Canyon de Chelly is remote and is one I would cut. Mesa Verde is awesome and if you go, be sure to visit Durango. It is one of our favorite places to stay. This sounds like a wonderful trip and we wish you a safe trip. Good luck.
Mesa Verde is awesome and if you go, be sure to visit Durango. It is one of our favorite places to stay.
This brings up a good point. Some great scenery isn't even in the national parks. The area north of Durango up to Ouray including Silverton and Telluride is some of the prettiest in CO. Likewise, while Arches and Canyonlands can take up a fair amount of time when visiting Moab, the "River Road" UT 128 is worth the drive, including the LaSal Mountain Loop if you have the time. Plan your route carefully to see some of these beauty spots, which often have less crowds and are more "wild".
Every time we make that kind of trip we spend more time and cut where we go. We spend more time at each place and see many great places that are close to them that do not get much notice because they are not National Parks. Make a smaller circle and see more.
Have time to rest.