Absolutely! If you can't find something to do on the ship during port stops, you simply aren't looking.
Unlike some cruise lines which use saltwater in their pools (which I understand must be emptied before entering a port), DCL uses fresh water, and the pools remain open.
The restaurants follow the same schedule as they do while at sea, including the buffet on the 9th deck.
There are activities throughout the ship, such as tours, lectures, demonstrations and games.
You could also treat yourselves to some spa treatments onboard.
Check your daily Navigator for a comprehensive list of what's available, or simply plop yourselves out in the sun and relax.
On our last cruise, when we stopped at Key West (where we've been many times) we went ashore for only an hour or two, then returned to the ship and enjoyed the pool, hot tub, and simply lounging and enjoying a good book while sipping a

.
We're going on a 3-nighter in October, and our group of 4 plan on staying aboard during the Nassau stop - - been there, done that.
And enjoy your "people watching"; sometimes that's a major highlight of the entire trip!