That's a very good question!!!!
see Post 2170 flight manifest, TIST is the closest major airport, On St Thomas then a short boat, seaplane or helicopter trip from there, probably the same way they got all the building supplies to build tunnels, temples checkerboard walkways etc :^)
Has to land in St. Thomas, then short hop via boat or chopper to the island. No landing strip on St. John either.
Might be able to land on St. Croix.