You don't have to have ever stepped onboard a cruise ship to know that the ships themselves are massive and packed with things to do. Cruise lines are always opening new attractions on their ships to see what guests enjoy doing most. However, you should avoid going to these attractions early if you want to save a bit of money. They'll likely be at capacity during the start of a cruise.
That means there won't be any discounts until the long lines die down, and staff needs to keep the attractions operating at capacity. This will also help you avoid long lines.