Folks,
I doubt the Tetons are largely empty right now. Ha. That just doesn't happen around here in the summertime. Maybe up USFS gravel roads, but not in these popular national parks.
I'll bet reservations are now required at most campgrounds, but if you are trying to find a pay campground in GTNP or YNP on a first come basis you need to be there mid morning when people pull out. At Bridge Bay campground in YNP last week there were ten camper trailer vehicles waiting in line to use the dump station so they could head out. So something like an hour wait just to dump the camper and roam on.
I was down that Jackson way last week minus the Rpod, via YNP from Cody, and it was pretty jammed up traffic wise, with lots of campers and trailers. The usual July rush. Jackson was a huge traffic mess, big city traffic not moving, as always this time of year until September.
Granite creek is a good choice should you be going south of the Wind's. And the hot springs are great.
They cost to get in though. Downstream a bit from the commercial operation you can find a great free place to soak.
If going thru Lander/Dubois then once you go over Togwotee pass and get to the bottom of the mountain you will cross the Buffalo fork river after a few miles. On your right following the bridge about a half mile is a nice paved narrow road that goes up Buffalo valley. The same road eventually turns gravel and ends up high, back at the Togwotee mountain lodge up on the highway below the pass. You can pull an Rpod the entire way and make a circle. Kinda bumpy and rough on the dirt road. There are several dispersed camping sites along the Buffalo fork road near the trail heads and in places where you will find pull outs. You will have to check the USFS postings on where you can and cannot camp, but lots of horse people pull in and camp there and take day rides or longer trips from their base camps. Free, beautiful views of the Tetons from some locations. Plus you can watch the horses and outfitters big horse pack strings headed into the wilderness.
Not quite like Stone Mountain GA. country, eh? Or the Blue Ridge. Enjoy Wyo.