Less expensive options for flying are SLC (4 hrs 45 min to town of Jackson via Soda Springs - route not recommended at night) or BZN (4 hrs 7 min to town of Jackson and 3 hrs 21 min to Driggs which is 22 min to Targhee, all according to Google maps). These give you opportunity to ski Utah or Big Sky before or after Jackson. Note that all times do not include food or gas stops or delays due to icy roads or storms. Flying to one of the more distant airports works better if you are sharing the cost of a rental or best if someone can pick you up and give you a ride. There are bus options from SLC to Jackson.
Searching today from San Jose showed one-way, one-stop Delta flights from SJC to Jackson were $296 and BZN was $95. Non-stops to SLC on Southwest were $69/79,so flying into Jackson is 3-4 times as expensive from where I live.
A problem some people have experienced flying to Jackson is flights can get canceled or missed due to storms at Jackson or airport on the way like SLC or DEN, or baggage, especially skis, can be left behind if on smaller plane from SLC. Then you can be stuck scrambling for alternate way to Jackson or waiting for airline to get you or all your baggage on another flight.