Batik Fabric
 

Going on a cruise to St. Thomas and heard there was a
Batik Factory there. Would anyone have info on it and
where it might be on the island.

Have you Googled? I think it's this one on St. Kitts:
http://www.caribellebatikstkitts.com/

The only two Caribbean batik factories I found were Cabrille on St Kitts that Prism mentioned and Androsia on the island of Andros in the Bahamas. http://www.androsia.com/