You're right, it is a broad question! What you're wanting to do and see will dictate when you go. My favorite time to go out west is in the fall. You have hunting seasons in, the Elk, Bear, and Moose are in their prime, the aspens will be turning colors about the 1st of Sept. and continuing throughout the month, and due to school back in session the numbers of tourists will be down from thepeak of summer. If you visit Yellowstone or Rocky Mountain N.P., you will see hundreds of elk with bugling bulls gathering their harems. Bear and moose will be a little more difficult to find butif you look in the right areas you may find them. Snow will be on the peaks of the mountains. The temperature will dipbelow freezing at night and daytime highs will usually be in the 60's-70's.
I hope this helps alittle, if you get more specific, maybe we can help more.