I've never contributed to chowhound before, but figure I'd spread the love...
I'm from LA, and just got back from Jackson Hole today after 3 nights, 4 days. After about 6 hours of serious research for restaurants on here, yelp, and tripadvisor, I narrowed it down to Rondevous Bistro, Snake River Grill, and Wild Sage at the Rusty Parrot Lodge for dinner, and Cafe Genevieve for brunch and the Amangani Grill for lunch.
If you're in a pinch, any will be adequate, but Snake River Grill I'd really go back to. Great service, nice setting, really great everything, you won't be disappointed.
I chose Rondevous because it was more casual and local, and it was just that. A lot of locals, really good service, good quality ingredients, but the flavor and the price were a bit off, I'm not jumping to go back, but it wasn't awful.
Wild Sage is the highest price point of them all, and is more refined in its style of cooking. I felt that the kitchen struggled to maintain a high level of quality it was after, since it was only 8 tables in there. For instance, they have great cheeses, but when we ordered a cheese plate, they were all too cold. We were probably the only people who ordered a cheese plate that night, so they couldn't afford to take up any space in their small kitchen to keep it out. That was kind of the feel of every dish. Good intentions, high quality, well trained, but always fell short of what they were aiming for.
Cafe Genevieve is great for brunch, casual, good service, kind of like a modern greasy spoon. Its a limited brunch menu, though, and 7/10 of the dishes are bacon/pork. Luckily they had a salmon benedict special, because I'm not the heavy breakfast type. But I'd definitely go back.
The Amangani was a beaaauttifffulll space with a deck overlooking the valley. They seemed to have a bee problem, so much so that they warned us about sitting outside. I'm sure it was just seasonal, but we moved inside halfway through the meal. It was definitely pricey, but they had formal service and good food. Not amazing food, just good. But if nothing else, go for the views.
We also stopped by Jackson Lake Lodge for lunch. Their mural room restaurant has amazing views, but don't go out of your way to eat there.
All the dinner spots I would recommend getting reservations for, they are surprisingly busy, even at the the end of the season.
and as a side note, if anyone happens to stay at the Best Western Plus, AVOID BREKFAST AT ALL COSTS...I didn't stay there for food, and everything I read about the place warned about the crowds fighting for terrible scraps, but it was really the worst hotel breakfast Ive had in a decade.