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.
Cascade Springs is a large artesian spring with naturally-terraced cascades and pools, located in American Fork Canyon. Over 7 million gallons of water flow through the springs each day. Cascade Springs isn't a hike, but more of a really easy, casual stroll.
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. You will likely not see another hiker which is great, but the biggest downside to this route is the amount of dirt bikes. We passed seven of them by 9am, and the noise and dirt they kicked up wasn't the best, and I had to make sure I moved Charlie far enough off the trail. However, if you can get past that you will get a huge reward in scenery and views on Mill Canyon Peak.
Ibantik Lake ("eye-ban-tick") is located conveniently close to the Mirror Lake Highway in the High Uintas, and backpacking this route is perfect for beginner backpackers since it's a fairly short yet rewarding trail. It is a very popular lake to camp at, and therefore you won't have much solitude. The best things about this lake is how clear the water is, and you'll see plenty of mountain goats as Notch Mountain looms above you. The trail is really easy to follow, and is best done as a point-to-point route.