You don't say if you are on a 3 night or 4 night. I know on the 3 night Dream cruises, the Mixology and other tasting classes are on the Nassau day. On the 4 night, they might have tasting classes on the Nassau day, but I can't say for sure.
Use the Rainforest Room in the spa. You can pre-purchase day passes through the In-Room Gifts & Amenities section for $16 per person per day.
Ride the Aquaduck. In my experience, a lot of people stay on the ship when it's in Nassau so there will still be a line, but it will be shorter than when not in port.
Hang out in the adult pool area.
Check out Navigators from disneycruiselineblog.com to see what else might be offered during that day.