I've been several times in mid-Aug, late Oct, early Nov, Thanksgiving, mid-Dec......by far the worst time was last June. We were there from the 18-26. It was brutally hot/humid, and the crowds were huge. I can deal with one or the other, but not both!! My dh was with us for the first 5 days, then it was just my 11 y/o dd and myself. At one point my dd turned to me, after eating breakfast at CP, and said.."Can we just leave Mom? There are too many people pushing me and it's too hot!!" This was at about 11 a.m.!!
Would I go during June again? Yes, but I would be prepared for the crowds. I would not spend as much time in the parks and more time doing other stuff. This is a time when a lot of people can go rather than mid-Aug when a lot of schools are back in session.
So, be prepared for a lot of people and very hot and sticky weather.