Eastern California Museum, 155 N. Grant St (three blocks west of the historic courthouse), ☎ +1-760-878-0258 (firstname.lastname@example.org), . daily from 10 AM to 5 PM. The Eastern California Museum features a diverse collection of artifacts that reflect and illuminate the unique history of Inyo County and California’s Eastern Sierra region.Free, donations appreciated. edit
On the west side of US 395 four miles south of Independence (ten miles north of Lone Pine). 
Manzanar was the site of an Internment Camp for people of Japanese ancestry during World War II.
In time of war, it is normal and accepted practice to imprison or confine citizens of an enemy country who reside in the opposing country. The Japanese Internment of World War II went far beyond these reasonable bounds. During World War II, all people of Japanese descent living on the west coast of the continental United States including American citizens were stripped of property and most belongings and sent into imprisonment at remote locations in the West.
To properly understand why this improper internment happened, one first needs to understand some background: California had a significant history of racism against Asian peoples including preventing Asians from participating in the gold rush, blaming Asians for economic bad times and getting Japan to voluntarily reduce emigration to California, and forbidding Asians from owning land.
The Manzanar Relocation Camp is the best preserved example from this deplorable episode in American History, and is slowly being turned into a National Historic Site.
In some Asian cultures, there is a severe injunction against being a troublemaker or being out of step with good behavior. For such Asians, to be interned or jailed is a mortifying embarrassment. If you should happen to meet someone who may have been interned, keep in mind that this embarrassment may (or may not!) apply.
West of town on Onion Valley Road is access to the Sierra Nevada and the Pacific Crest Trail via Kearsarge Pass. Take Onion Valley Road to the trailhead; the pass is some hours' climb farther up. Above 11,000 ft, the air becomes thin. Fall colors along Onion Valley are very nice, for California.
From the Pass, the views are empyrean- to the west, the Sierra, and to the east, the White Mountains, Last Chance Range, and others into the Great Basin.
The Winnedumah, on 395, is a historic motel and is charming. Rooms can be a bit small. Some share a bath, some have private baths. There is a prix-fixe dinner some nights, and a "cocktail hour" where your first glass of the house wine is free. Cooking is quite good. There is also breakfast (moderately priced).