After Labor Day, some of the CGs in Yellowstone will be closing, and many of the ones inside the park won't have room for a rig your size. I recommend Grizzly RV in West Yellowstone - just outside the park boundary by only a few blocks, and has lots of pull-thru FHU sites for big rigs. Nice place to stay, and it makes for a good base camp for the park. I suggest a reservation, but I suspect that if you're going to be there much after Labor Day, it won't be essential as long as you arrive by 4 or 5 PM. (I almost always make reservations anywhere, but that's just me - I don't like unpleasant surprises.)
Renee is right, crowds are down but not gone, and many of the hotels, shops & restaurants in the park are still open. Depending on how late in September you go, you may get some fall color in the aspens, and you just might get a chance to hear elk bugling. Whether or not you get snow, you should be prepared for freezing temps overnight in the park, since the altitude is high (7000-8000 ft; West Yellowstone is at 6600 ft.)
Are you talking about 2-3 weeks total time for the trip? If so, take 3, minimum, and plan to spend about a week in Yellowstone & the Tetons. (You can take a day trip to the Tetons & Jackson from West Yellowstone; we've done it, with time for a picnic, lots of photo stops, and ice cream.)