First week of June was our first family trip several years ago. It rained (afternoon thundershowers) almost every day. Weather was hot but not terrible. Crowds were bearable. We had a great time.
FYI...1st weekend in June is traditionally Gay Days at MK (on that Saturday). We saw nothing offensive- just lots of homosexual groups (all week really). We chose not to go to MK that Saturday once we found out. Had no idea this was scheduled time for that as it is not sponsered by Disney but, from what I understand it is a yearly occurance.