We were there in late September, so we missed some experiences that you will surely enjoy. We drove to Jackson from Rapid City SD via Yellowstone Park. The parts of Yellowstone then were unlike our previous experience. I can only say that it was "Closed". Even the animals were gone - no buffalo, no elk, etc. Really spooky. We did see a buffalo on the highway into Yellowstone walking along in the right hand lane all alone!
We did get to see some antelope and a small herd of buffalo on the Gros Ventre road - someone tipped us off about it. Gros Ventre Road is probably the only suggestion I can give you for anything different than what you will surely see, but the scenery there is very nice and you do get a different view of the Tetons along the way. A couple shots taken there are on my Smugmug site under travel/Jackson Hole. I have to confess that that
gallery is only partly finished.