May 20th...but...if I were you, I'd buy the Unofficial Guide and use their online planners that have historical attendance information for the dates you're considering.
The fact is, if your kids are out of school, there will be tons of other kids out, too. And, while locals makes a huge difference in CA, I don't think they have that kind of impact at WDW.
I'd cast a wider net...and the Unofficial Guide will let you do that!