Frankly, as a native Californian....I'd be apt to drive myself, unless I was under real time pressure...at which point I'd fly. While I understand that you come from a country which drives on the other side...it wasn't such a major switch for me going the other way.

I'd certainly avoid taking the bus.....since the only bus service is Greyhound, which has *terrible* service.

You could fly....although the airports (LAX, LGB, SNA) are rather distant from the Anaheim/Buena Park area, and if you don't plan to rent a car, you will need to rely on horrendously expensive taxis, somewhat pricey shared van services, or very poor public bus services.

Actually, if you have the time, taking the train is not a terrible option...although the trip will take a rather long day. (10-14 hours by schedule) The cost is comparable to flying ($60-65), and the distance from the Anaheim train station to is *less* than that of traveling from an airport. Make sure however that you take the "Coast Starlight" rather than the "San Joaquin," since the former follows the scenic Pacific Coast much of the way while the latter travels through the boring Central Valley farmlands...and requires a lengthy bus connection to LA.

For information on Southern California public transit, you should look at http://socaltransport.org/tm_pub_start.php , which will do public transport trip routing in the Greater Los Angeles area.