I stayed in Lone Pine July 17-19 and did a couple of day hikes in the area. On Day 2, I decided to hike to Kearsarge Pass, with the possibility of trying Mt. Gould. Unfortunately some weather rolled in as I was hanging out at the pass, so I decided to save Gould for another day.
Here are some hightlights. Clicking on any of the photos will bring you to my full trip report and gallery (~60 photos):
From what I remember, Flower Lake @ about 10,500 is probably going to be the last place for you to get water. You'll see a sign and path for Matlock Lake. The lake closest to the trail is Flower Lake. The water in the lake itself looked murky, so you may want to pull some from the inlet or outlet.