It is a beautiful time to go and fewer people. It can get chilly/cold at night and don't be surprised to have a little bit of snow depending on how late in September you get there.
Highly recommend staying in West Yellowstone, MT at Grizzly RV Park which is just outside the west entrance to the park. Depending on how much time you have for travel and what else you want to see, there are several ways to get there and a lot of beautiful country all around YS.
At the southern exit to YS is the entrance to Grand Teton NP and the Tetons are not to be missed while in that area.