We go in June almost every year. Traffic is less than April through May, much less than during the height of winter. You can look at the cruise calendar here, but ships in the Caribbean in general in the summer are ALWAYS less, because some ships go to Alaska and some to Europe. As far as children, many schools don't get out until mid June. When we go in June we don't see many children. By the time you get to August, it gets pretty humid and the chance of a hurricane is always more in August. In June and July, the water is warmer, less people, just about perfect to us!!