seeing sharks other than nurse sharks? --- well, the best places in the Caribbean are Bahamas and Turks & Caicos. Both places have Caribbean reef sharks and hammerheads along with an occasional tiger or bull. Best chances to see them is from a liveaboard but you can see them from day-boat trips also sometimes.
In the Pacific you can see white tip sharks in Hawaii, and
every kind of shark in Palau or Fiji.
