If you're hiking Whitney a few days after arriving in the Lone Pine area, I would recommend a day hike in the Horseshoe Meadow area. The meadow is at nearly 10000 feet and there are several trails leading up to passes a few miles away (for example, Cottonwood Pass is 11200 feet and 7 miles round trip). It's a great place to hang and get acclimated and it's only a half hour from Lone Pine.
