GD,
We the did Tetons and Yellowstone last year late Sept on our way to Kansas.........and it was fantastic! The National Park fee will allow you to use both parks for one week. The fall colors are in full force, very few people, no problems getting a campsite without reservations (check which ones are open.... they have closing dates posted on their website). We camped at Fishing Bridge (hookups available) in Yellowstone, and Colter Bay (no hookups where we camped) in the Tetons. The nights are cold! We exited Yellowstone via Sylvan Pass, which had certain hours of use posted, extensive construction ongoing, and was a bit harrowing as it was steep, narrow, bumpy, and muddy. If you're planning on using that route, check ahead on the status.
I've included some pics of what you'll expect to see at that time of year!
Have a great trip!