Can you expand by what you mean by "long distance"? The indigenous population of the Caribbean was active in traveling between islands and various areas by boat. Columbus describes the canoes when he first encountered the Lucayans of the Bahamas, he described their water craft as "a long boat all cut out of a single log. They are marvelously carved... and they are so big that forty or fifty-five men came in them." (Cohen, ed. Four Voyages of Columbus, p. 56; I refer to the natives as Lucayans, as I agree with Charles Hoffman's argument that Columbus first landed in San Salvador in the Bahamas. Hoffman, "Archaeological Excavations at the Long Bay Site" in Gerace, ed. Columbus and His World; Craton & Saunders, Islanders in the Stream, Vol. 1; Keegan, The People Who Discovered Columbus).

Outside of the Bahamas, the rule of thumb for historians and archaeologists of the Greater Antilles is that the indigenous people will have more in common with the people across gulfs of water, than people on the same island (Wilson, The Archaeology of the Caribbean).