I'd be inclined to consider public transportation (using
www.metro.net) only if I had no bags. You wouldn't see much along the way. I agree with those who suggest at least looking into a one-way car rental. You can stop along the way if you so please, dump the car at LAX that evening, and stay at a hotel near the airport (you can get good deals through Hotwire or Priceline or, since it's Xmas Eve, maybe find deals on hotel Web sites). Don't know if it'd be open Christmas Eve, but the Encounter Restaurant in the spider-shaped building in the middle of LAX is kind of interesting, with great views of landing and depating planes
http://www.encounterlax.com/ Finding restaurants open that night may be tough anywhere, but hotels with restaurants/bars should have some food available.