Most people will do the Dunn River Falls tour on their first visit to Jamaica. The ship will be offering other tours on the island as well. I'd recommend you do one through the ship, so you won't be worrying about getting back to the ship on time.
The Jamaica Tourism board has been working very hard to overcome the stereotypes people have about their island. I have been to Jamaica many, many, times on cruises and last October spent four days there at an all-inclusive. Jamaica has a lot to offer if people just give it a chance. Does it have some problems? I don't know too many places that don't have some type of problem. Jamaicans are very friendly and welcoming people.