I have fished all over the Rockies in UT, ID, MT, WY, and CO. They all have their + and -, but over the last couple of years I have found myself returning to Colorado.
I now prefer the hike-in, backcountry pursuit of the native cutties (yes, dinks). I also prefer the beauty of Colorado's scenery (and it's 58 14ers) to all of the other states. If you were looking for hike-in fishing, Estes Park would definitely be number one on my list! Hands Down!
Durango is a great area and early September would put you on the early kokanee run (I hit it last year at Roaring J). From Durango you are also not far from the Conejos and Rio Grande headwaters. My recommendation would be the I-70 corridor somewhere in the Front Range. I have never stayed in the Dillon/Silverthorne area but you would be within a couple hours of the Colorado, Arkansas, Eagle, Frying Pan, Roaring Fork, South Platte headwaters, RMNP, etc. Some of those tailwater streams can get crowded but you are talking about BIG wild fish!
Another option you may consider would be Wyoming and the official Cuttslam. I stayed in the Hoback area a couple of years ago when I did the Cuttslam. From the Hoback area, you are within a couple hours of some very nice waters in WY, ID, and Yellowstone. You would need to hit the park or the Cody area to pick up the Yellowstone cutt, but other than that you have the Snake, Greys, Hoback, Gros Ventre, Teton (ID), Henry's Fork (ID). The official Wyoming Cuttslam certificate is first class, the Wyoming Fish & Game have a very nice program in this.
I've fished MT from "base camps" in Big Timber, Bozeman, and Dillon. They are all nice and I have never had an issue with crowds, because everything is so spread out.
Again, just my opinion and I don't think there is a wrong answer.