I too will vouch for West Yellowstone area being the most economical place to stay in the Yellowstone basin. Be certain to get your motel room early in the day. As in prior to 3:00 pm.
The inexpensive motels are the first to fill up. As the day turns into night, the more expensive ($100+) rooms will be the only ones you'll find available.
You should know the 2nd week in September is no longer the summer season in Yellowstone. Indeed, snow is possible. Perhaps even likely. Prepare accordingly.