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At Cozumel I would recommend the Royal Swim with Dolphins at Chankanaab Park. The park is a $10 cab ride from the pier and then you pay entrance to the park (cash only) we booked direct with www.dolphindscovery.com and saved money over the similar excursion offered by RCCL. If the beach is your thing then there are numerous, Nachi Cocom is a good place to go- Google it- have time for shopping in town and go to Pancho's backyard for lunch. If you want a raucous good time go to Margaritaville, Senor Frogs or Carlos 'n Charlies, all on the main seafront road. Anything you want in Cozumel is about a $6- 10 cab ride away from the pier.
If you do enough research beforehand on each port then this is not an issue. Haiti is Labadee - their own private beach - you do not get off the beach. All others are easy to do by yourself.
I agree with Aldrich from Newbury, do your research before hand,everything is easy to do by yourself, however we did everything with RCCL. We booked on line before hand and everything was so well organised we did not have to waste time looking about, deciding what to do etc. At the end of the day it may have been slightly more expensive, not much I have to say, but hey your on a cruise, go and enjoy. The beach buggy drive in Cozumel was real fun and the stingrays in Grand Caymen are not to missed and if you really want a thrill try the zip ride in Labade.