Early summer is better than late because of the hurricanes and storms which tend to be more intense from July on. There are some cruises which incorporate a cruise and stay in the Caribbean and some which include places like Orlando, LA or Las Vegas or you can have a 7 /10 day cruise and pick your own spot to relax within striking distance of where you dock or further away again if you want to pay for the transport. Let's face it....The world's your lobster init.. Neil.
Some cruise lines do not operate in the Caribbean during the summer months because of the possibility of hurricanes. The hurrican season lasts from April to November. Additionally the summer is very hot and humid in the Caribbean. You would be much better going between December and March if this is possible for you.