Not many people in Sept

There are not that many visitors even at the end of August. Two years ago, we could get lodging at the Old Faithful Inn the same day at the end of August. You will have a great time there, be sure to stay in Old F I for one night and visit the geyser hills at dusk and dawn. The experience cannot be described. The lodging is a little pricy, but well worth it. Do not try to save money by staying outside the park. Old Faithfull is the most famous (and predictable) geyser, but there are so many others that are much grander (though not as predictable).
I rank Yellow Stone, Arches, Capitol reef the best parks I have ever visited. Much better than some of the other popular ones (Yosemite, Grand Canyon)