Now, Anaheim has conventions all the time, so this may not make a difference, but...
June 24-27 is USA Gymnastics National Congress (national convention of gymnastics professionals), to be held in conjunction with Olympic Trials (most important domestic competition of the year, choosing the Olympic team, so there will be a lot of fans).
That's why I'm going then! June 18-28 for me!
My bet is that the beginning of June would be less crowded, as summer vacations from schools are just starting to get underway then.