Many people find that the best time of year to visit the Cayman Islands is during the winter months, and hotel room rates certainy reflect that (rates from Christmas through Easter are much higher than the rest of the year). During the winter, the temperatures are consistent around 75-85 degrees farenheit., with humidity at a comfortable level.
Many savvy travellers choose the shoulder season after Easter but before the temperature gets hotter and more humid.
The switch from "dry" to "rainy" season tend to happen around mid to late May, at which point things tend to get hotter and more humid right through until late October, when the seasons switch around again.
As all Caribbean afficianados know, June 1st to November 1st is Hurricane Season, so one should watch out for weather systems etc (and take out travel insurance with some of the savings from the low summer hotel rates!), but not be put off by the (low) risk of a tropical weather system disrupting their vacation, particularly as an increasing number of resorts are now being more and more flexible if visitors need to rebook due to threatening weather.
The slowest time of year is September, but this is also a time to get great rates, and for divers the visibility is normally the best of the whole year.
Winter visitors are mostly from the Northern and Eastern states of the USA, whereas in summer those from the South and South West find the Cayman temperatures (low 90s, light breeze by the ocean) relatively cool !