Bruce's idea of using Mammoth is ok, but it adds 1.5 hours to the drive from So. Cal. Two nights at Whitney Portal would be ok, but you are technically limited to one night for the walk-in sites. You would need to pack it all up during the day.

I'll often drive the 5+ hours from my residence all the way to Horseshoe Meadows, often arriving late at night. But I do take a half a 125 mg Diamox that morning and night to help with acclimatization. I'll also take a sleep aid (benadryl is my choice), because it's hard to sleep the first night camping anywhere.