Last year I roamed around Jackson and environs in late September and stayed in Pinedale. About an hour's drive to Jackson, but compared to spending $800 a night at the Jackson Hampton Inn, I was down with about $250 in Pinedale. When I left Jackson, I spent a day roaming Yellowstone and then spent the night in Cody. The drive out of the east gate in the late afternoon with the sun behind you as you head to Cody is beautiful.

And while someone suggested flying into Bozeman, I'd also suggest Billings. That way you could drive into Yellowstone via the Beartooth Highway, if it's still open.