Backpacking to Titcomb Basin in Wind River Range of Wyoming should be on every backpackers "to do" list. The rugged terrain offers massive mountains with spire towers, clear glacial lakes, high alpine grassland & wildflowers, and world class hiking, backpacking, and climbing. Titcomb Basin is truly a pristine and special place.
Hayden Peak (12,479 ft) stands out for anyone who's driven along the Mirror Lake Highway in the Uintas. This rugged peak is quite intimidating from the road, but for Peak Baggers that's nothing to prevent us from climbing it. Hiking to the summit of Hayden Peak is NOT for the beginner hiker nor the beginner peak bagger. You should be comfortable hiking across narrow ridges, class 3 scrambles, and route finding. There is either a very faint, or non-existent trail. Though this route is only 2 miles one way, you'll gain a total of just over 2,000 ft.
Mill Canyon Peak (10,349 ft) sits on the backside of the Wasatch Mountains and offers amazing 360 degree views. For a 10,000 ft peak this is a relatively easy summit - there's a trail most of the way and no scrambling.