Ah, the best three things about a teaching job - June, July, and August!
Peak season? If you go by the cruise fare, June is about as high as it gets. Temperature hasn't peaked, seas are relatively calm, lots of demand by families wanting to get started on summer vacations. I think it is a great time weather-wise to travel, very warm but not too much (and the ocean breezes abord ship and on the beach tend to take care of that anyway).