For me, rum from Martinique is the ultimate. (Clement, Trois Rivieres, La Mauny) It's distilled from cane juice, not molasses, and so has a very different taste. Brazillian cachaca is similar. Since the French side of St Martin is part of the same "department" of France as Martinique....maybe they'll have it there? You can bet I'll be looking since I'll probably be back to St Martin before I make it back to Martinique.
Another St Martin specialty is infused rums. "Ma Doudou" is one label. In the tall skinny bottle was dark rum, some bananna slices, cinnamin stick, and vanilla bean. This made an excellent after dinner drink.
Jamaican rums have a very good reputation, although I am less familiar with them.
All in all, for me, the fun of being in the islands is getting stuff you can't get here (including rum from Cuba). Killer bargains on Bacardi, Meyers, etc, are fine, but I go for novelty! That includes at trip to Guavaberry rum shop in Phillipsburg, St Maartin.