If Yellowstone may be part of your plans, check its website for road closures as well as what activities may be occurring. By October, roads may be closing for the winter, but the winter transports (Sno-cats, etc.) may not be running that early. Thus, you may have very limited access to the park. Getting to West Yellowstone to access the park from the West would probably take you a couple of hours from Jackson, assuming the pass is open.

In Jackson, however, the elk heard may be gathering there by then. The other things to do in Jackson (shops, a few museums, etc.) probably won't take more than two days at most. So depending on if the weather allows you to do things outside--whether walking, hiking, biking, or snow-shoeing--will probably make a big difference. Also check Grand Teton's Nat'l Park's website for activities there during the period you're considering. Snowmobiling usually doesn't start in YNP until December, but I don't know when the operators start running the Divide trails.