There are no true anchorage around the south side of Virgin Gorda as they aren't really protected.
The furthest south would be Spanish Town, where you can either pick up a
mooring ball or
anchor.
Next would be Savannah Bay, which is beautiful and empty but you need to thread in between two
reefs and I
head that a sailboat was sunk there when a squall line came through at night. I've always wanted to spend a night there but as I'd like a spotter while going in through the reef I've never gone. How much does your
boat draw?
If the
weather were truly settled one might be able to
anchor (in sand, of course) around
Coral Gardens to the south side of Great Dog island.
That sums it up, the next closest anchorages are going to be Trellis/Marina Cay and the North Sound.