That's a lot of driving, and I like driving. But a lot of it is scenic.

If you stay in Markleeville you can ride the Death Ride passes for a couple days without driving.

For the eastern sierra passes I'd stay in Bishop, and move to Lone Pine to do Whitney, Horseshoe and Onion Valley. Get rooms early in Bishop- starting in September there's a lot of events that fill the rooms. That's the nice season there.