Is it that you are flying west on Tuesday and have until Saturday to travel from the airport to Story, giving you 4-5 days to travel in the area? If that is the case and it's from Billings and the weather was co-operating, you could visit Yellowstone and the Tetons and then to Story through the Bighorn forest/rec area. You could head out to Devils Tower, Mt Rushmore, Custer and the Black hills etc, even Badlands NP, but going both directions might leave you a little stretched for time. I don't know if Rapid city would be an option to fly into, but that would put you close to the Black Hills and then perhaps you could include a brief visit to Yellowstone as well before heading to Story.