I did a Wonder and a Dream 3 night cruise...
Nassau is....ummm....in family friendly words...BORING...
As you've never been I'd get off the ship and wander around. But keep any valuables on the ship. Avoid taking a handbag at all. There is nothing to see in the SAFE areas really other than shops. I think all the excursions are way over priced. If you want to play with Dolphins then go to Sea World Discovery Cove.
There have been and continue to be muggings of people who venture out on their own and there have even been hold ups of segway tours.
DBF's friend was mugged in the Caribbean when he ventured just slightly off course because he forgot something.
The Dream cruise I stayed on the ship and ENJOYED THE PEACE AND QUIET!!!