Kate...
Forget the transit system to get from Anaheim to downtown LA or the Getty...you must rent a car.
LA's transit system is all over the map. literally. The subway, which is the newest element, only goes to and from certain areas, and none of them are near Anaheim, which is in a different county from LA. When people take the subway, if they don't work near a stop, they have to take a bus or walk the rest of the way, ie, in downtown LA there is basically just one subway line going down one street, that's it. It's not like NYC at all...
It takes a long, long time to get to places when using the LA system unless you are near a stop and going to a place with a stop nearby.