In Ocho Rios either stay on the ship or walk down the pier to Margaritaville, get some drinks and use the pool or use the beach for a few bucks. The Dunns river falls is fun too and you'll have plenty of time to do both. I have done other excursions in Jamaica from this port and cannot reccommend any of them.
In Georgetown, Grand Cayman, I'd avoid 7 mile beach, too crowded and touristy, hotels everywhere. I'd go to Rum Point. There is a ferry that will take you there quicker than a cab and will be much less expensive. Just ask a local when you get off the ship. And though I've not been, Stingray City is supposed to be really great. Some of our friends said that it was the highlight of thier cruise.