For the BVI's, Terrance B. Lettsome International Airport (EIS) is located on the British Virgin Islands' island of Tortola, accessible by a short water taxi ride from the marina on Scrub Island and a land taxi to the marina in Road Town.
Alternatively, Cyril E. King Airport (STT) is on the US side of the Virgin Islands from where you can take a ferry to Road Town. Just remember you'll need to go through US and British customs.