There are now moorings availible near Christiansted harbour. Crime is not likely to be a problem unless you are out too late. Use common sense, stay out of dark places, and try not to over indulge.
Green Cay marina is secure, with fuel/water, and helpful staff.
To 'legally' anchor at Buck Island you need to get a
permit from the National Parks
service in Christiansted. It's free.
You can also anchor off the west end of the island, usually calm during regular trades.