Here is a site for shore excursions. One of many.
http://www.belizecruiseexcursions.com/
The cruise line will offer one as well. Disembarkation with a ship load of people is like a stuffed subway in Tokyo.
Stay on the main streets in Belize City if you explore. The back streets have barbed wire compounds where the wealthy drug lords stay with bodyguards.
Check out the American retirement villages if you have a desire to locate and of course snorkel where permitted if possible.
Have a great time!
John_AZ