I just got back from a December cruise, so maybe I can help.
I'd saay take a short excursion. I took the "best of ocho rios" ($45 each), and it was relatively good and not very long. We went to some plush ruins, Dunns river falls and the last stop was Margaritaville, which is in a nice shopping area. From there you can walk back to the ship. What ever excursion you pick, check how long it is. One group from our ship took a excursion and it took them 1.5 hours to get there, do the tour and 1.5 hours back....that was way too long.
If you go to Margaritaville, be ready for $10 hamburgers and $5 beer. Don't even think about a mixed drink, it's cheaper on the ship. There are small beer joints where one can grab a cheap beer.
I had heard of all the horror stories about the natives bothering you and everything, but that never happened. It was quite enjoyable. Just stay on the beaten path and everything will be fine.