I need to amend my previous post. I highly recommend that you try and fly in a day early. Los Angeles is so spread out that getting to the areas that you want could eat up most of your time there. Whether you try and rent a car and drive or find a tour that goes where you want to go, you still will be dealing with long distances. And the traffic can be as bad as its reputation, or worse. It can take anywhere from 1-2 hours to get from San Pedro to Pasadena, for example. Plus, if you are driving, unless you know your way around, don't try taking side streets. There are some areas that are best to stay out of.
That said, I have always enjoyed San Pedro itself. And they used to have a trolley tour where you could hop off and on at various stops.
Keep us posted about your plans as they develop and I will try to help you make the most of your time there.