In Nassau you can book tours privately and we recommend looking at Shoretrips
since they are normally cheaper than the same tours offered by the cruise line. Doing stuff at Atlantis is probably the most popular.
For Coco Cay you have no option other than booking excursions with Royal Caribbean, since they own this 120 acre island. It is a big beach with a barbecue lunch. Doing a jet ski rental is the most popular. I would probably rent one of the new private cabanas and just hang out.