I'm also going the 2nd week of June, and expecting it to be pretty crowded. I'll be getting to the parks as early as possible.
While I don't think there's a crowd calendar available, the "wisdom" I've heard is this:
If it's crowded at Disney, it will be crowded at US - but a little less so.
People tend to go to Disney early in the week and then head over to US/IOA, Sea World, etc.
So:
Wednesday should be less crowded than Saturday. Also, if you're planning to go to Disney, too, Saturday is generally one of the best days of the week over there.