Shoy's Beach
One of the most beautiful beaches to visit on St. Croix is Shoy's Beach. Quiet and relaxing, it is almost completely abandoned during the week. It can be reached through the Buccaneer Resort.
There are no amenities available on Shoy's Beach, so if you want anything to eat or drink you'll need to bring it with. Likewise, if you plan to snorkel, sit in a chair, or do just about anything else other than walk or lay and soak up rays, make sure to bring it with - there are no rental booths or anything of the like. Which, of course, is what makes this such a great beach to visit. Just you, the waves, the sand, and the fresh breeze.
The eastern end supposedly offers the best options for swimming, while heading the other way to the western end of the beach should reveal the best snorkeling to be had in these parts.