When we stayed out there Dick, we stayed at the Flagg Ranch Resort and Campground. It was right by the South entrance ( nice location) for day trips up into yellowstone. We've also stayed around Jackson Hole a couple of times, but found it to be "a drive" to the park. On a map it doesn't look far, but you have to factor in all the tourist traffic.
Flagg Resort was rather basic, but we could wash clothes, buy ice, eat out if we wanted to, etc.
A huge bonus - the views of the Tetons to the south just a short walk to the S edge of the campground.
PS - we did always reserve FAR ahead of time when we visited JH or Yellowstone.