A beautiful loop to consider, at Lone Pine, 4hrs drive, Horseshoe meadows campground, popular start for hiking the john muir trail, golden trout wilderness.
Drive to the campground, park. Hike to the cottonwood lakes area, just below New Army Pass, fantastic views, plenty of lakes to pick for camping, beautiful and EASY trail, about 4.5-5miles.
Be advised almost all the camping/hiking anywhere in the easter sierras will be above 9000-10,000' so altitude must be a consideration.
It's possible to make it a 2 night loop by going over new army pass and looping back over chicken spring lake, excellent trail system.
Use free caltopo.com maps to highlite your trails and print a map. The ten essentials are mandatory (well, not mandatory, but I highly recommend), bear canisters are required. Permits at recreation.gov (search inyo national forest wilderness permits, then select horseshoe meadows or cottonwood trail heads, one is for direction of new army pass, the other is direction of chicken spring lake)
Here's a link to the caltopo.com map I worked up when planning my JMT trips.
<iframe width="100%" height="500px" src="https://caltopo.com/m/7N6N"></iframe>
REI member since 1979