This is a pretty big subject and would take many pages to answer completely.
One of the answers is dependent on what time of year you are traveling. Junkanoo is a cultural experience around the Christmas holidays.
there is something bush medicine that is cultural born, mostly available in the Out Islands.
Sponging, conching and lobstering are done in The Bahamas in ways that you don't see in other cultures.
there brand of caribbean music is 'different' than other islands in the Caribbean also.
there are historical sites to see such as the fort in Nassau, the Hermitage in Cat Island, the cave where the Eleutherans sought shelter on Eleuthera when they first arrived in the 1600's.
The columbus monument on San Salvadore.
Each island has some history attached to it that makes it unique.
