If you decide you only can do an excursion in one port - do it in Belize City. The other ports are easier to DIY. Was in Cozumel last week - it was $7 for a taxi to town if you want to shop. You can also head to the beach as well.
Check out the Caribbean forum for more ideas on these ports.
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, Royal 2017
Star Clippers: Royal Clipper 2015