Use a Rental Car and drive to Titusville for the most excellent Rock Shrimp and Hush Puppies at DIXIE CROSSROADS. Plenty of time in port to use the car for driving around to see all the important sights. Otherwise, there are taxis for hire and shore tours.
A tender day to go ashore for famous sun/sand/surf and beach picnic. Don't forget your towel, SPF, and clothing protection. Limited shade from the sun. OK to bring your own chair umbrella from home. Limited souvenir shopping. Bring water toys and shovel/pail for the younger set. Shore tours available, if you are so inclined - otherwise, a relaxing private island.
Many options on foot, private hire, or organized shore tours which are always recommended. Walk to town. Leave your valuables on the ship, in the safe. Take small bills or Credit Card. Be alert to your surroundings and Enjoy all that Nassau can offer.