I would scout during August and see many elk in the Flattops.  Then come hunting season they seemed to have moved down to private property.  One time in early August I saw at least 250 cows and calves.  Returned in 3 weeks and didn't see an elk in 3 days.  Yes, there were many other hunters after them.  I don't have any area I would recommend there.  But it remains a favorite place for backpacking.

I have to go with the Flattops also. It's been many years since I hunted there. We backpacked in over the China wall at the Devils backbone a couple of times and even as a young man it took alot of breaks climbing in and out. Still the prettiest area I've hunted in. I want my ashes scattered there, but probably won't have anyone in any shape to get them there!

Eagle's Nest is really nice country to.

When I lived in Colorado I hunted the Eagles Nest Wilderness a lot and loved it. The Mount Zirkel Wilderness is great also. Both areas are beautiful, rugged and full of elk. I made friends with a few gray jays in the Eagles Nest.