We just spent a most satosfying week in Jackson Hole. The off-season is great--there are very few tourists.
Lots if restaurants were closed but I still would not call Jackson a restaurant destination. Here is my opinion:
Grill at the Amangani. We stayed here and it's far and away teh best (and by a far, far margin, the most expensive) hotel in Jackson. Dedicated staff, great roooms and views, etc. The grill was probably teh best of teh Jackson restaurants and in a week we ate there 3x. Excellent main courses (venison, etc.) and a good pasta/vegetarian entree each night. Overpriced wine list heavy on big hitters and charming if slightly inexperienced and unprofessional staff.
Nani's Pasta House. Watch out for this one. Surly owner/chef, brain dead staff (don;t even try an Italian pronunciation), huge 'olive garden' menu which yields very poor standard dishes (amatrciana and so on). Main course of lamb chops severely overcooked, was told chef was Italian and did it that way! Slightly run down and dirty, too.
Rusty Parrot. Not bad but not worth a repeat visit. Some bizarre combinations (vodka, miso soup, and taro root or something like that?), small, ugly room, unprofessional staff, no espresso machine, and very limited wine list. Home-made ravioli had some flavor but were overwhelmed with a rich cream/garlic sauce.
Other: there's no place with decent cheese and bread in Jackson for picnic lunches. Albertson's appears to have teh best selection.