Good advice above.
My favorite place to acclimate is Horseshoe Meadows. You camp at 10,000', and there are some nice easy hikes from there. It is 20 miles out of Lone Pine, starting up the Whitney Portal road, then turn left to Horseshoe Meadows. Here's a
Trail Peak: Warmup / acclimatization hike description.
Since you are spending two prior nights at altitude, packing all the way to Trail Camp should be ok. But if your packs are heavy, you might do better stopping at Outpost. The advantage is sleeping lower (so altitude sickness issues may be reduced), and reducing the distance and fatigue of carrying heavy packs. Most people are able to day hike from Outpost to the summit.
