Easily the best restaurant in the town of Big Piney (although that is not saying much), is the Mexican-ish restaurant: La Cabana.
Be forewarned: The portions are huge! This is probably the single largest burrito I’ve ever (mostly) eaten. Kate got a large taco salad substituting black beans for beef. Our waitress was nice as well.
Definitely not a proactively veggie-friendly restaurant, but still a refreshing option in this Wyoming food desert.