You can pull any of these up on google by going to Tuttle Creek , then typing "hiking" in the maps search box: Mt. Whitney Trailhead, Mobius Arch, Arch Loop trail etc.

Not only good hiking, but interesting historical sites nearby like Manzanar and the Oyler House https://www.youtube.com/watch?v=ufk8JDIci1s

The cottonwood area has lots of trails. Very high.

We hiked down from Mt Whitney. It was gorgeous and followed a creek with waterfalls most of the way. I will caution you that the sign said 4 miles and our fitness tracker said 7 miles, so be prepared.

There is fabulous hiking from Tuttle Creek Campground. There is a lot of trail wandering in the Alabama Hills and a short drive up into the hills puts you onto The Pacific Crest Trail, John Muir Trail and the High Sierras. It is also near the launch point for trekkers up to Mt Whitney.

There’s a trail right out of the campground the leads west toward Mt Whitney. Plus lots of places to explore at nearby Alabama Hills

yes, you can hike up to and around Mt. Whitney, also some trails outside of Independence and a couple further up the road from the campground. Easily found on alltrails.com

All over the area...

The closet hike up into the mountains is the Tuttle Creek Ashram. Interesting history and a beautiful area. Nearby Alabama Hills and Whitney Portal are awesome also.

AllTrails shows 340 hikes near Lone Pine, CA! In particular, there are many different hikes up to Mt Whitney which can be a multi day trip.

Yes! Some easy, most moderate to hard. Great trails straight up the mountains, or through meandering boulders and beautiful pines. Forest service has a great collection of information in independence.

I'm sure there must be but I don't know as I'm not a hiker.