Now, obviously, I live in SoCal, where the parks remain open throughout the year, so these days aren't options for everyone (without travel). But I like the three-day weekend holidays during the school year because you don't have nearly as many out-of-market tourists as during summer, Thanksgiving and the Christmas holidays.
Veterans Day (in November) is the best, I think, because its proximity to Thanksgiving -- and Christmas shopping (when people are eyeing other things on which to spend money) -- keeps the crowds relatively small.
Another 'None of the above' here. I prefer not to visit any park over any major holiday. Too crowded, too noisy, too much.
My favorite time to visit any zoo, oceanarium, or (rarely) theme park is as far off-season as I can get without running into winter weather.
Happy travels.