The weather should be fine, but because it's the transitional season you could get some rain (then again we haven't had much rain the past few years). Temps in the 70's, it should be pleasant.
Yes, check out the Getty. Plan on spending at least a few hours minimum there. Go early, have some lunch. Maybe do that prior to your flight to PPT and get yourself good and tired so you can sleep on the plane. And yes rent a car, it's just easier.
For something different to do, there's the Queen Mary in Long Beach. If you've never been to it it's pretty awesome. I love the art deco flavor of the ship, it's pretty nifty and it's a good way to spend about 3 to 4 hours depending on how fast ya walk around soaking everything up.
If ya want a good "greasy spoon" type place thats close to LAX, go to Panns. It's food is good but its in an awesome building from an architectual point of view - total 50's diner which I think is cool.