Hi - my wife, myself and our 6 year old son will be stopping for the day in Falmouth Jamaica while on a Royal Caribbean cruise at the end of January. Two years ago, we stopped in Ocho Rios, and before the cruise, I asked the same question here, got alot of great recommendations, and ended up going to Dunn's River Falls and had a great time!
Despite enjoying cruising (it's easy with a young child and there's SO much to keep them entertained), we really try to avoid the "cruise cattle" mentality. Which means we never sign up for the cruise line excursions to get shuffled here and herded there with a hundred other people. When we reach a port of call, we'd rather take off and do our own thing.
So, any tips? Remember, we have a 6 year old, so ATV's, ziplines ... all that stuff is out of reach. Mostly just looking for somewhere beautiful, "relatively" quiet, with a clean beach and water to relax.