Very funny lifesaver.
A rental car is a MUST. LA is very spread out and public transportation is basically non-existant.
I'm gonna disagree wiith phisigduchess and say do not stay in Torrance. If this is your first trip to LA you're going to want to be in Santa Monica, Westwood, Century City, Beverly Hills, West Hollywood, Hollywood. Basically, you want to stay north of the airport, not in outerlying suburbs.
West Hollywood is pretty central--you're close to the best restaurants, great nightlife, great shopping, and 15-20 minutes from the beach. At this time of year Santa Monica and other beaches can be quite foggy early in the day, so a bit farther inland will give you better morning weather/sunshine to wake up to.