There are many long threads here and on WPSMB on the subject of acclimatization. My two cents: When you are acclimatizing, you should try to sleep at the highest altitude at which you don't get sick or have symptoms. Places you might consider (in order of elevation) include Mammoth, the campground in the White Mountains, the Kearsarge Pass trailhead, Horseshoe Meadow, and the locked gate before hiking up White Mountain Pk.
The best options for the night before your climb are Horseshoe Meadow and Whitney Portal. Sleep is important. Since you plan to start up super early, I would sleep at the Portal and get an extra hour of sleep.
Remember that your acclimatization hikes are for acclimatization. The last few days before Whitney are too late for serious training.
Good luck.
