Most everyone I know who drives through that area makes it a point to stop at the Yellowstone Drug Store or now it may be called Yellowstone Malt Shop in Shoshoni, Wyoming. It is easy to find in this small town and worth the stop.
Yellowstone Drug Store
502 E 2, Shoshoni, WY 82649
If you're in the very north of Idaho on Highway 20, the TroutHunter Last Chance Bar and Grill is DELICIOUS. Some of the best food in the area. In Island Park, Idaho and about 40 minutes away from West Yellowstone, Montana
You can check out some photos on my website of my dining experience there- you won't be disappointed.