The other area airport I haven't seen mentioned is Ontario.
Here's a list of the milage going the route I would normally go from each airport to
Disneyland.
John Wayne 13.2
Long Beach 18.5
Ontario 35.3
Los Angeles 39.3
John wayne is the easiest to get on the freeway, there's an exit from the airport that takes you right on the correct freeway to get to DL. You also only need to take 2 freeways, and it's relatively easy to get there from John wayne.
Ontario and Long beach would be a toss up. Its been a while since I've been to Ontario, and I think they've made it a bit easier to get on the freeway from here, but it used to be a pain to get here from the freeway, and get back to the freeway from the airport.
Long beach isn't hard to get to or from the freeway, but getting to DL is a bit harder. You've either got to go out of your way, or drive through some areas that aren't the greatest, have lots of traffic and stop lights.
LAX is a pain, but usually cheaper to fly into (although not always). The way we go would mean taking 4 different Freeways, and that can sometimes be a pain. Especially if you're anywhere near rush hour (which would be 6 am to 9 am and 3 pm to 6:30-7pm).
My number one choice would be John wayne, unless flying jet blue.
Just a word of caution on Long Beach, you go into a building to check in, then you go outside that building and walk around another building and go through security. This building has some gates, but most are in a different building. To get there you go out the building you are in and up a ramp into a trailer that has most of the gates. Then you walk out the door (you are again outside) and have to walk up the stairs to get on the plane.
When you arrive you walk down the stairs, into the building, out the building, into the other building, out that building, to the bagage area. The bagage area is outside (though if I remember correctly covered). Not all the walk areas are covered, so you would get wet if it were raining