In Cozumel, you can get a cab over to Chanakaab Park, not far from the pier....In Grand Cayman, any cab driver can drop you off at 7 Mile Beach...they will know the hotels that welcome cruise passengers...
Belize you could take an excursion to one of the cays were they snorkel, but you have to climb on and off a tender
All I ask is a tall ship and a star to steer her by; John Masefield
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014, 2016
Star Clippers: Royal Clipper 2015