We are chartering from island yachts.... When I emailed to ask about transport from airport they sent this info----
"You can take a taxi from the airport to our location in Red Hook (The American Yacht Harbor.) The rate should be approx. $12-$15.00 per person. Ask the VI Taxi dispatcher to put you in a cab going directly to the Red Hook area."
So it doesn't look like they have a dedicated taxi service. I will certainly call them to follow up to see if the have any additional info.
