Stay near Picnic Beach, which is the nicest beach on Big Corn Island. There are several hotels right on this beach, including Martha's Bed and Breakfast and Picnic Center Hotel. These hotels will give you good access to a gorgeous strip of sand.
Eat fresh seafood from any of the beachside restaurants. Everything is cooked fresh and to order. Caribbean fish curry in coconut sauce is a local specialty.
Go snorkeling on any of the reefs just ashore. You can sign up for snorkeling tours at several of the hotels, or with the Nautilus dive shop on Big Corn Island.
Take the boat to Little Corn Island and spend at least a couple of nights there. Little Corn is more rustic, and even more picturesque than Big Corn, and offers excellent snorkeling and diving opportunities.
Enjoy the freshly baked coconut bread and cinnamon rolls that are sold by little girls at the ferry dock on Little Corn Island.