Seconded! We visit in very late May / early June every year, and it is one of our favorite times to come to the island. Is the weather a bit hotter? Sure. However, you're avoiding peak hurricane season by months still, everything is open on the island (as already mentioned), and (best of all, IMO) all of the hotels and rental car agencies are offering low season rates that are often as much as 50% lower than what you would pay in December through March.
Because it is off-season, you'll also enjoy finding parking far more easily during peak hours, easily getting into the most popular restaurants, and beaches that often have only three or four other people on them.
Have a wonderful trip!