If you plan to go to Yellowstone as well you will want to do so early in September as almost all the campgrounds inside the park shut down by mid-September. No such problems in the Tetons.
Changing colors of the leaves depends upon when the cold weather hits and that is anybody's guess. This year the snows melted very early and Tioga Pass in Yosemite was open by the middle of May as were the other mountain passes in California. It is never all that predicable and hardly going to get easier with the forces of global climate change taking effect more and more across the USA. Best to be prepared for anything weatherwise.