The Allure of the Seas is a large ship, to say the least. There are a number of activities in which you can participate.
You can “surf” on one of two FlowRiders or swim/splash in one of the pools.
You can ice skate (there is also an ice show).
You can climb one of two walls.
You can go zip lining (it’s short, but high).
You can play in the arcade.
You can ride the carousel – yes, there is an actual carousel you can ride on “The Boardwalk.”
There are other activities, too. There are “game shows,” contests, the card room and library, the casino, cupcake decorating, food demonstrations, etc. Some cost extra, but most are included in your cruise fare.
The activities are not always available, and some are closed due to weather. For example, if it is raining, you won’t be able to use the zip line. If there is lightning you will need to leave the pool (but you can still swim if it is only raining).
I’m pretty sure you can find something to keep you busy on those sea days.