In late August the crowds start to thin out. September is great, and depending where and at what altitude you travel, early October can be really nice, although cooler.
Years ago we did a big circle from Denver to Mesa Verde, Grand Canyon, Zion, Bryce, Salt Lake City and back to Denver in the first half of October. Weather was fine until we got back to Denver when we had three inches of snow around the 17th of Oct. That doesn't last long, though.
I'd reccomend September if it fits your schedule.
'14 Winnebago Vista 35F, '14 GMC Terrain
BlueOx Towing Pkg, SMI Stay-n-Play
49 States & 7 Provinces visited in MH | WIT W112365