Brynne: Welcome to WhitneyZone! I hope someone will comment on your hike out of Horseshoe Meadows. You're certainly in for a treat. (You have a lot of miles planned -- pack light!)
I am just curious about your travel after the hike... First of all, Inyo National Forest is on the east side. I assume you will then drive north and cross into Yosemite at Tioga Pass. (The drive up 395 is a treat!)
If you could find the time, a side trip into the White Mountains out of Big Pine (east of Bishop) will definitely give you a different geological perspective. The Bristlecone Pines are a unique forest -- only growing in dolomite formations.
And Sequoia N.P. is on the west side, except you will be stepping into it from the east when you ascend Cottonwood or New Army Pass.
Sequoia has some unique limestone caves -- check out Crystal Cave, open to public tours.
