You definitely want to do your primary grocery shopping in Idaho Falls. Take the Broadway exit off of I-15 and turn left at the bottom of the ramp. There will be a strip mall with an Albertson's on your left in about three blocks (second stop light, IIRC).There will be a Flying J gas station on Broadway on your right, which is a good place to gas up.
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This area is very heavily LDS, particularly the areas outside of Idaho Falls. If you are a coffee drinker who enjoys higher quality beans, I suggest you bring beans with you, as selections in grocery stores is often quite limited. In Idaho Falls the grocery stores might carry some of the Starbucks blends, as well as some roasts from White Cloud roasters in the Sun Valley area. Outside of IDF it's pretty hit and miss for being able to get a decent cup of coffee.
I think there is also an Idaho state liquor store in the same strip mall on Broadway in Idaho Falls as the Albertson's I mentioned above; there was one there when I lived in that neighborhood about 13 years ago. (If you want distilled spirits in Idaho you need to go to a state liquor store.) If you don't pick it up in IDF, you can probably forget about it; there's nothing after that. I haven't even found a restaurant in Rexburg that serves beer and wine. Possibly there might be something in St. Anthony; I haven't spent enough time in that area to be familiar with what is available there.
If you want to eat out, your best options will probably be in West Yelllowstone.
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Geologically, that is an incredibly interesting area. Yellowstone is a volcano that is a hot spot in the earth's crust, somewhat similar to the hot spot that creates the Hawaiian Island. As the North American crustal plate drifts over the hot spot, the hot spots creates a 60-mile wide gash in the crustal plate. The Snake River Plain in Idaho is that gash.
The figure below shows the route you will take from Ashton to Island Park. Note the semi-circular area of mountains that I highlighted in yellow. Those mountains are the remnants of the Island Park caldera, which was created when the Yellowstone volcano was active in that area. That Island Park caldera became inactive when the volcano began erupting at it's current location in Yellowstone Park. The east side of the Island Park caldera has been obliterated by the Yellowstone caldera eruptions.
So as you cross the grade north of Ashton and enter the flats, think about the fact that you are entering an inactive caldera of one of most violent and destructive volcanoes on earth.
