Planning 1st Trip to Yellowstone: Getting there question

You can't go wrong with either east or south entrance. There are a bunch of fs cgs within 3-15 miles of the east entrance and Grand Teton has a bunch too. If you want to see your options in Cody, Jackson, the Tetons, or Yellowstone this is the best tool for planning: Yellowstone area campgrounds and rv parks

Also look at Dubois that is a pretty route and a bit out of the high traffic area.