I love SNA ( Santa Ana / Orange Country ) and LGB ( Long Beach ) for Southern California arrivals and departures.
Even if you have to pay a little more in airfare to fly to one of those airports instead of LAX....DO IT.
You WILL thank yourself ( and all of us ) later on.
If you HAVE to use LAX, use it as a arrival airport ONLY...as in, you are flying IN and then departing via ground transportation to Anaheim.
You may well have to deal with some insane traffic to get to Anaheim, but that will be nothing compared to the experience you may encounter going through the LAX security screening if you were flying OUT of LAX.
Take my advice - book a flight to SNA or LGB instead and save your sanity and good standards.
LAX has all the charm and ambiance of 'a third world prison built by Communists' as a fellow Forum poster here once elegantly stated.
Now, unlike LAX, John Wayne/Orange Country airport has real charm and true ambiance - beautiful, functional, rarely crowded, and just a nice place to spend some time.
This is a airport you WANT to hang around in for a while.
Bright and friendly feeling with plenty of decent restaurants, snack places, services, and shopping options.
It is about a 30 minute ride from SNA to the Disneyland Resort, slightly more if their happens to be a lot of traffic ( rush hour, etc. ).
I highly recommend SNA as a great option for arrival and departures !
Long Beach Municipal is a slightly smaller airport, but was recently renovated and is now downright classy.
Since there are not as many flights serviced at this airport, there are little to no crowds.
Another plus is you get to arrive ( or depart ) like The Beatles...and step off the airplane right onto the tarmac via a set of rollaway stairs.
Sure beats the standard gate arrivals elsewhere!
For ground transport, i recommend SuperShuttle.
You can book your ride in advance via their website and be all ready to go once you arrive.
I have found them to be very reliable, have friendly and helpful drivers, and most importantly very reasonably priced.
You can knock the price down even further if you do a quick search online for current discount codes.
Disneyland does NOT have a 'Magical Express' bus service in regards to the service provided for Guests who room at one of the WDW Resort hotels.
There used to be a 'Disneyland Express' run by Grey Line out in California, but i found the service to be very unreliable ( pick ups to return to airport ) and the price a bit above what i would consider 'fair'.
Not sure if this service still exists....i heard recently they had stopped but another bus company is now handling the service.
I would recommend SuperShuttle over them any day regardless.
I hope the above helps some....and i wish you a fabulous time at Disneyland !
You might well end up yet another 'Disneyland Convert' that gets a taste of the REALLY magical experience to be had in California and 'gives up' WDW...!
Many folks have over the last dozen or so years ...self included!
Enjoy!
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