I second the nomination of the Hampton LAX.

I often fly out of LAX early in the morning. When I do so, I return my rental car the night before, sometimes saving a day's rental and always minimizing what I have to do in the morning. While you can get from any car rental company to the Hampton by taking the car rental company's shuttle into LAX and the Hampton's shuttle back out, some car rental companies (in particular Avis) will also just drop you at the Hampton. With Avis they drop you in a separate courtesy car, not the big bus, so you have to ask for this at the check-in counter--don't just get on the bus and ask to be dropped at the hotel.