I lived there for over a year and never seen many, if any boats, anchored off of Frederiksted for a long period of time. That part of the island is well protected from the trade
winds but does not offer any other sort of protection.
Here are some options:
Christiansted Harbor: You'll be right in town, good restaurants and bars, shopping
, access to public transportation. It can get crowded.
Green Caye/Tamarind Reef Marina: Nice marina and walking distance to the Tamarind Reef resort. Not sure if they have transient slips. This will put you 5mi or so further east of Christiansted.
River: There is a small marina and area to moor but don't have any details. Pretty isolated.
East end: There is a big anchorage on the North side about 2 miles from Pt. Udall. Protected but you're a loooong way from Frederiksted.