Well it's five hours from the Bay Area to Kings Canyon. For a hike that actually replicates the continuous elevation gain and distance, it is well worth the drive. I've never done a Whitney Hike without at least one practice hike in the Sierras like that, I'm too afraid of failing if I don't!
As for traffic, there isn't much if you leave around 2-3 in the morning. Just go to bed early if possible. Besides, you may as well practice sleep deprivation because that'll be a part of the Whitney experience.
