Welcome Jeanna, You don't always have to do an excursion in every port...I would do some research at each port and see what interests you. You can look through the Carnival web-site and see what they offer.
If you haven't already been to Grand Cayman, I'd suggest snorkeling with the sting rays at Sting Ray City, a really great time. If you do enjoy snorkeling, Belize has some great tours and also the rafting...
At Cozumel, you can take a cab over to Chankanaab Park and spend the day, great beach and they offer the swim with dolphins which is also a lot of fun....
On our recent trip we went for a tequila tasting at Casa Mission, in Belize we flew to Ambergis Caye and did a snorkeling trip, and at Mahogany Bay we just hung out on the beach.
Like Donna said, you can start with the Carnival excursions. Then search for tourism websites for your destinations. You can also look for independent tour sites such as viator. Search the term shore excursions and add your destination.
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
Star Clippers: Royal Clipper 2015