I, too, will say that my port dining has not been a problem at all. In Nassau, even the ice cubes fared well. I had no problems in the small eateries and bars, and in the large hotel restaurant. You should not have to worry.
Don't be foolish and eat from a street vendor, unless you get sealed product that you open. Even bottled water can be refilled. Make sure you break the seal.
Enjoy Nassau. It's so lovely. The view from the fort is wonderful. The sun rise and sun set is beautiful. And that flea market is tight and crowded, but well worth the walk through. Stick to the culture and history and touring, it has a lot to offer.