Agree with others. Book an airport hotel (there are lots), take the hotel shuttle bus from the airport and just 'crash' at the hotel. Unless you travel really well, you'll be glad not to have much hassle / navigate LA's freeways when you arrive. Once you check in and freshen up you can get a cab to Manhattan Beach for a walk or anywhere else, depending on how you are feeling.
Airport hotels at LAX don't charge the huge premium like Australian ones do.
I often stay at the Sheraton Gateway Hotel on West Century Boulevard - its one of the closest to the airport (and therefore one of the first drop-offs), but not any more noisy. One of the advantages of hotels in this area is that you can then walk to several of the car rental lots - certainly Avis, and I think also Budget and National (I think). So the next day, just walk over and pick up your (pre booked) car. However if your rental car place isn't one of the close ones, just catch a cab or the free shuttle back to the airport, then get on the rental car's shuttle bus!
The free hotel and car rental shuttle busses pick up outside each terminal at variously coloured 'zones' and these can be a bit chaotic. There are usually volunteers at the outside exit from TBIT who are there to point you in the right direction. Couple of dollars tip is probably worth it. Hotel busses (they drop off to hotels in a particular area, not specific to any one hotel) can be confusing, for instance there might be several Sheratons serviced and different busses might do each. Make sure you get on the right bus (just ask the driver).
This may sound confusing, but don't be discouraged. Just keep your eyes peeled and you'll be in the hotel in no time. Then start afresh the next morning.