I would never suggest anyone live close to Jackson Hole unless you are well off or live like a ski bum. Since you're single you might be able to find some recently divorced sugar momma
This ^^^. Living in a resort town has some major downsides no matter what state you are in unless you make a living off tourist.
As to the OP you won't make it in Wyoming on $10-$13 an hour IMO. If you have any construction, welding, equipment operating, CDL, etc skills you will be able to make more money.
As far as jobs you will probably want to look for the bigger cities that have been mentioned as opposed to the smaller resort towns which will have limited year round job opportunities. Places like Cheyenne, Casper, Rapid City, Billings etc will have much more to offer than Pinedale, Jackson, Encampment, Saratoga, etc... Cheyenne has some real advantages being the state capitol, having an air force base, and a refinery.