I know of one off the N entrance of Tetons. I spent a year near West Yellowstone and led some backpacking trip in the area. Don't recall anything along the road between the two.
There is a large fs campground outside of Jackson Hole to the east. To get to it one drives along the elk preserves so side. I camped there once back around 1980-81. It was a typical fs campgound.
Atherton Creek Campground
Forest Rd 30374, Kelly, WY 83011
When one clicks google maps show similar places a bunch come up. See attached screen shot.
-.- . ——- .— - -.-