We normally book through the ship, but a lot of people have posted they have truly enjoyed their excursions when taken with Shoretrips. You can book when you get on the islands as well, but you're not going to save anything. You can google both ports and turn up loads of vendors. Shoretrips is based in the US, according to one of our members.
In Jamaica I strongly suggest sticking with a ship's tour. In Grand Cayman you can do it on your own. Captain Marvin's is another popular tour operator there. Bear in mind that Stingray City can end up looking like Time Square on New Year's Eve with all the tour boats. Earlier is usually better.
I guess I am the one woman promoter or Shoretrips.com. They are based in Wisconsin, I think. We have had a lot of good experiences with them. I am not a fan of large groups, lines, or crowds and those were all what I experienced going through the ship's tours. We have become more and more bold about going on our own with private vendors, however, Shoretrips.com claims to have never had a patron miss a ship. I guess that is the primary concern when I leave the boat each day--I want to be aboard when she sails! We did stingray city 4 times--twice with the ship, and once with Captain Marvins, and once with Captain Ron (he was shoretrips vendor). The last two trips were a lot less people and a better time to be had. We have also used Ebank's watersports (web site) on Cayman and can't say enough good about these guys. I would check their offerings.
I would use the ship, or shoretrips.com on Jamaica. THis is not a place I want to be on my own, with strangers, or stranded.
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We just returned from Grand Cayman and used Moby Dick tours for Stingray City. Their early excursion had a total of 40 people. We were on the second excursion, which had a total of 32 people and left at 11:10am. Our tour took 3 hours and cost $40. Just before we were getting ready to leave it did start to get a little crowded, but our group was small and had a lot of interaction. Nicholas and William were great guides. At our request their bus dropped us at Seven Mile Beach. Taxis were lined up and returned to us at our ship at a cost of $5.00 per person.
As Dave mentioned...stick with the ships tours in Jamaica. We did the family White River tubing ...it was a blast. Our local guides were also giving us tips on who to watch for and whom to speak with. Grand Cayman was and extremly safe....did the Atlantis Sub ...very cool. My 2 cents....I'm a law enforcement officer here in Michigan near Detroit and the only time my little "caution alarm" went off in my head was in the side streets of Ocho Rios. Don't get me wrong.... just keep both eyes open. Both places were very beautiful.