We loved the Midship Detective Agency game. It was so fun! My son did all three mysteries. Turns out you can even repeat them and get a different culprit at the end, so you can really play as much as you want.
Aquaduck is a blast! If you can stay on the ship for awhile when in port one day, you can ride without waiting in line.
Play a round of mini golf. The course is pretty easy, but the views are gorgeous and it's not every day you get to play mini golf on the 13th deck of a ship!
The midship elevators get very crowded at dinnertime, so walk to the front of back of the ship. However, make sure you get a chance to ride the two glass elevators at midship at some point during your cruise. You'll see some cool artwork inside (take a ride all the way from bottom to top or vice versa for the full experience).