As you are seeing, there are ENDLESS possibilities on Hwy 395. Since you live so far away, I would expect you would want to capture as much of the Sierras as possible. If you are hitting Death Valley, why not camp at Mahogoney Flats and hike Telescope Peak (good acclimation)? Climbing Whitney is quite an accomplishment, but as others have said, why not take the JMT to Kearsarge Pass (Onion Valley)? The Rae Lakes could be on your list, or hikes out of Big Pine or Bishop (South Lake, North Lake, Sabrina Lake), there are hikes out of Mammoth and all the way to Yosemite (not that far from Lone Pine). Why not hike the Panorama Trail from Glacier Point to Little Yosemite Valley and back to the Valley (Yosemite is a zoo until you get out of the Valley)?
You need more time off!