Along that route through Eastern Sierra, I would strongly consider a visit to both Devils Postpile National Monument and Manazanar Interment Camp National Park. I personally think both places are amazing visits.
If you are into trout fishing the June Lake Loop, previously mentioned, has great fishing. But more importantly in Devils Postpile is the San Joaquin River, which is still designated as a "natural wild river" with native trout.
I certainly wish I could spend several weeks exploring that area, we are still exploring a week or two at a time due to work and kids schedules.
