September is my favorite time of year to go to Yellowstone.
Long, long ago, when I first started going up there, you could count on empty parking lots, empty roads and plenty of campsites after Labor Day. Not any more.
The number of visitors in the fall has skyrocketed, but the park service has not really adjusted the campground fall closing times to take this in account. The result has been more campers chasing after few campsites.
Last year I arrived at Pebble Creek campground on a Wednesday of the third week in September, just in time to get the last available campsite - at 10:30 a.m. On that same trip I also stayed at Norris campground and Tower campground. Both were completely filled by the early afternoon.