I live about 5 minutes from the Getty and I have to admit that the views from the Getty as well as the building is amazing; however, the Norton Simon is the better museum if you wanted to see a better art collection (at least in my opinion).

Public transportation is difficult in LA and very time consuming. I would suggest renting a car or using one of the two shuttle services from LAX -- either the Supershuttle or Prime Time. It should cost about $25 each way. Good luck!