If you have the time, use US 287 all the way from Dallas to Grand Teton and go through the Yellowstone South Entrance. Tbere are many great places to camp in mid-September in Colorado and Wyoming along that road and you should be hitting the peak of the fall aspen leaf change.
A wonderful campground to stay in just before going through the South Entrance is the Colter Bay RV Park on Jackson Lake in Grand Teton National Park. You will go right past it on 287, so don't pass up the opportunity to spend at least one night there. The RV Park, as opposed to the Colter Bay campground, has electric hookups, which may come in handy if the weather does turn cold. And, if you don't already have a reservation, check campground availability in Yellowstone now because only a couple of their campgrounds have electricity and all, or some parts, of them may have already closed by the time you arrive.
Incidentally, we are going to be in Cody, Red Lodge, and Thermopolis at the same time you are going to be in Yellowstone! And I have worked in Yellowstone, including one mid-September when it did snow, and have been there numerous times since. So for other campground suggestions along US 287, PM me and I'll try to help out.
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