In case you find yourself on Highway 395 between Bishop and Lone Pine, I am happy to recommend the Still Life Cafe in Independence.
As far as I can tell, the restaurant's ownership recently changed hands (and names), so I don't know how long it's been open. I would recommend following the link to the restaurant's phone number and confirming they'll be open when you want to go. In any case, the new owners are French and offer a nice menu, especially noteworthy because I didn't encounter anything similar for miles around. The prices seemed in line with a metropolis (entrees in the $15-25 range), but if your palate needs more than hamburgers and pizza, this place is a real find.
The restaurant has a pleasant atmosphere, including a piano which was in active service last Friday evening with a range of tunes from Autumn Leaves to Fats Waller.
In case you were wondering, Independence is the county seat of Inyo County and boasts a population, according to the sign when you enter town, of 1000 people. The Eastern California Museum in town is a loving scrapbook of the region's history.