Hike to Lost Man's Pass in the Hunter Fryingpan Wilderness. Enjoy the views at Independence Lake (and Lost Man Lake if you decide to make a loop). In the summer the area has a wonderful wildflower display. To Lost Man's Pass and back is 4.5 miles with ~1200 feet of gain. If you make a loop including Lost Man's lake to the lower trailhead is about 11.5 miles. From the pass there are several 13ers that can also be climbed and stay at class 2/3. However, class 4 options are available in the area.
Park at the pull out just west of independence pass. From there, begin on the Linkin's Lake Trail. The trail is generally easy to follow (although it can be muddy as it is a wet area) and climbs 900 feet in the 1.8 miles to independence lake. From Independence lake it is about 0.5 miles and 400 feet of incline to the pass. The trail stays to the west of the lake although there is a use trail that encircles the lake.
If you continue down to lost man's lake and down to the lower trailhead it is an additional 6 miles to the trailhead across from lost man's campground on Highway 82.
To access the 13er's in the area there are no official trails but in some places climbers trails will lad through the scree and talus. You can access the mountains of the cirque in any direction. Just be careful as the summer sees many storms above treeline.