I have the large double door Norcold fridge/freezer. I hit up Costco for ribs, chops and brats, then use my vacuum bagger and load up the freezer. Also usually have a big bag of frozen chicken breasts, frozen burgers, veggies, and a couple all-in-one meals in there too. I carry canned chili, soups, spagetti sauces, pastas, Ramen noodles, and several Knorr instant pasta side dishes in the pantry. Also always have burger and hot dog buns on hand. I always have a package of good ole hot dogs in the fridge as my go-to emergency food, as well as various shredded and whole cheeses. I buy hamburger and produce locally.
I carry two grills - a small Weber charcoal grill and a Green Mountain Grills Davy Crockett pellet grill/smoker. I think having a good grill is KEY.
Good restaurants can be found everywhere - that's why I like to carry frozen food as opposed to multiple days of fresh food. And 24 hour Walmarts are everywhere too.
You will be several miles from anywhere at Devil's Tower so definitely need to have meals with you, but Cody has everything (gateway to Yellowstone). I would not do the major provisioning till I got to Cody. It's been a while since I was at the Tetons, but know Jackson is close enough for re-provisioning or for a restaurant break.
I full time so YMMV.