i personally like yellowstone in the fall. I lead my trips in sept. You have the beautiful fall colors and the mammals are in the rut. they also have thicker fur coats etc. it is great hearing the elk bugling in the morning fog. it a memory you will never forgot.
if you go to yellowstone between july4-labor day you will get a lot more traffic and less wildlife
i would also consider going in the spring or winter'
don't forgot to visit the grand tetons also
good luck with you trip
Slonina Nature Photography