Wow... Edge and detective agency are the two my 13 yr old loved. But he also loved the Aquaduck and the independence. We trusted him on the ship, so that gave him the freedom to make decisions on what and when he did things (within limits, of course). The biggest was probably the ability to make friends and hang out with them.
But he (and my 15yr old) also loved the food, the ice cream, the movies, and the great service in the MDRs. Neither of my kids are 'relax by the pool' guys and while they did venture up to the mini golf/basketball court, I think it was often too windy for them to enjoy those activities.
I can tell you that they never went near the atrium or shops without me, as they are not character guys or shoppers.
I think they also enjoyed our beach excursions, as well. The older one went fishing with his dad instead of Castaway Cay and loved that, too, while the younger loved the water slides on Castaway Cay.