If your flight is delayed, there are hotels near the airport. One of them is Flat Creek Inn, a free airport shuttle is offered, but reservations are necessary. Hours are depending on the time of the year. Another one is The Lexington At Jackson Hole, which is 12 minutes from the airport, reservations are necessary at least 24 hours beforehand.
When you arrive at the airport, there is one restaurant, Jedediah. The working hours of this restaurant are from 5 AM, until the last departure of the day. You can find eggs, bacon, pancakes, breakfast burrito in the breakfast menu, and those dishes are served until 10:30 AM. If you are thirst, you can find a full-service bar and worth to mention that the coffee is fresh all the time. There are some unique local dishes which may be attractive to you.
Some ATMs are located near the luggage claim. Fees may apply; you must check your bank’s fee schedule and your daily withdrawal limit if you are moving internationally. Wireless internet access (Airport Public Wireless) is offered throughout the airport. There are no currency exchange boards, and you must try to do this before you arrive there. Drinking water fountains are provided free of charge, which is located both Landside and Airside.