There is some public transportation, but it is quite inconvenient. I recently returned from a trip to Los Angeles, and I have to say that a rental car is a lot cheaper than using cabs. A 3 day car rental for me came out to about $134, taxes included. I brought my own GPS to use and rented a Prius to save on gas. Cab fares will depend on traffic, and I am not too fond of sitting in traffic and watching the meter go up.

LA is not like Chicago and NYC where it is easy to hail a cab off the street. Almost everyone who can drive has a car, and those who cannot drive have to rely on public transportation and budget extra time for travel. This post has more info on why it is hard to get around metro LA by using public transportation. Metro LA is around 1700 square miles, which is an larger area than the state of Rhode Island (the smallest state in the United States).

I would recommend a visit to the Getty Center. It is closed on Mondays and open until 9 pm on Fridays and Saturdays. Admission is free, and parking costs $8. You could easily spend a day here taking in the art and strolling the grounds of the museum.

If you are not going to rent a car, you should stay a hotel near LAX that has a free shuttle to and from the airport. This will also make it easier for you to access public transportation. I stay at the Renaissance LAX when I visit LA because it is soundproof and the concierge lounge is open every day.

It should not be too hard to visit Santa Monica from an LAX hotel with public transit. That city is quite walkable, and there are a lot of restaurants, beaches, and shops to visit.