Just back from a cruise with one day on St. Croix. Sandy Point is great. However, we could not find any taxi driver who would take us there. They were saying it's closed (I knew it is open on Sunday as it is not turtle season) and the road is bad etc etc. We were not even bargaining about the money, just wanted to find anyone who would take us there. Then one diriver said he would take us there and pretended to do so. He left us at Coral Hotel and the walking distance to Sandy Point on the soft sand was too much for my friend with all the beach gear (towels, water, snacks, cameras etc). I went but had very little time to enjoy the gorgeous beach because of the long walk.
So either rent a car or otherwise make sure in advance you get there.