As already mentioned, ticket prices vary widely; one of the main considerations is whether more than one airline flies into/out of an airport. Jackson is served by one or at most 2 commercial airlines - less competition = higher prices. Bear in mind that changing airlines can be a hassle (especially if one of those airlines has to be booked separately from the others - it may mean that luggage can't be directly transferred, etc.) Just something to think about. You'll need to shop around. Other choices (not necessarily less expensive) that are within a day's drive of Yellowstone:
West Yellowstone MT
Bozeman MT
Billings MT
Cody WY
Jackson WY
Idaho Falls ID
Pocatello ID
SLC UT (the largest of the bunch) - 300 miles to West Yellowstone (one way)
Something to consider if using SLC or the Idaho airports is the Salt Lake Express shuttle vans/buses. There is service from SLC through Pocatello and Idaho Falls all the way to West Yellowstone and prices are pretty reasonable, so a car rental may not be needed (and would be more expensive). These are scheduled shuttles.