Hello caribbean, and welcome to cruise-chat.com!
Of your ports, the ones I've been to are Cozumel and Great Stirrup Cay, multiple times each. Years ago, we enjoyed a shore excursion to Tulum out of Cozumel. If your family is interested in history, this may be a good choice. I'd book this through the cruise line given its distance from the ship, and it is also a long tour. Should you decide to stay in town, there's great shopping and a nice restaurant at Los Cinco Soles/Pancho's Backyard.
Great Stirrup Cay is a beautiful beach, and I think that non-swimmers would enjoy it, as well. The waters are usually pretty calm, so "getting your feet wet" isn't too intimidating. We've taken several nice walks along the beach. Definitely bring sunscreen, and apply it often. This is the only place I have ever gotten a sunburn. (Ouch!)
One major thing I'd be aware of on the ship is its rules regarding 18-year-olds. In short, he will be able to use the casino and, with your written consent, purchase beer and wine but no other alcoholic beverages. More on this topic is in the NCL Guest Ticket Contract
Again, welcome aboard!