If you wanted to avoid the pass on 287 (not a biggie for us), then from I-80 go to Rock Springs and take 191 into Jackson and then through Grand Teton Nat'l Park - you ARE going to stay there, also, aren't you?
Just south of Jackson are a couple large grocery stores if you need to stock up before entering the parks. Smith's is on the left and I think it's Albertson's on the right a little further toward Jackson.