LAX is awful. Do anything you can to avoid flying into or out of LAX.
John Wayne is the first choice for a Disneyland trip, because it is so close and such a lovely airport. Long Beach is a good second choice, mainly because JetBlue has lots of flights there and the airport is small and easy and convenient. Third choice is Ontario; a new, moderately sized airport that is clean and friendly, but a bit of a drive into Orange County or Los Angeles. Burbank is next, as it's like Long Beach but quite a bit farther away from Disneyland than Long Beach.
Did I mention you should avoid LAX like the plague? LAX is huge and overcrowded and dirty and sprawling and ugly and a bit scary. The freeways radiating out from LAX are 16 lane nightmares. The sole redeeming quality of LAX is the fabulous Theme Building at its center. It was built in 1964, looks like something from The Jetsons, and has a fantastic restaurant and cocktail lounge in the top called Encounter that was designed by WDI. If you have no other choice but to use LAX, at least give yourself an extra hour to see Encounter and experience some of Walt Disney Imagineering's finest interior design work ever. The miniskirted hostess who loads you into the bizarre elevator for the ride to the top is worth the trip alone. (They did this Jet Set Mod restaurant in the 1990's during a very brief period of time when WDI was contracting out its services to locations not on Disney property or owned by Disney.)
Disneyland in August should be lots of fun. The weather will be dramatically better than the entire East Coast at that time of year; no humidity, not a drop of rain until December, not a cloud in sight with sunny, dry, hot days and warm, wonderful nights. And the new Submarine ride will be open, plus the new Pirates Tom Sawyer Island and the revamped Pirates of the Caribbean ride. And all of the other fabulous things that makes Southern California famous around the world.
Just avoid LAX.