Should the port just not be of interest to you, staying on the ship is an excellent way to enjoy it without the crowds. The pools are never as empty, the restaurants so quiet or the spa treatments so available as when the ship is in port. So there are many advantages to staying on board. Whether you purchase a cruise line shore excursion or wing it on your own, the cruise staff is always happy to recommend the best options for you. They know what's available, so take advantage of their knowledge.
Kids love cruises.
The down side is, you may find out how independent your youngster is without you. Obviously some cruise lines cater more effectively to children than others. But those who do, offer tremendous structured programs divided into age groups. They even offer shore excursions for the kids, so mom and dad can do the adult thing. Many programs are even offered in the evening.