For great snorkling you pretty much need a tour. The tidal waters of the Belize river makes the water around the port very brown. You will need to take a tour that goes to a barrier reef. There are many to choose from and there are also many little islands.
What the rest had said is correct. But to make thing clearer, the shopping village you tender into is for cruise tourists only. So the ladies could shop without ever having to go out into the true city. But even if they wanted to, it would be ok.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013