I have been to all three places.
billybuzzy basically said it all. I may repeat what billybuzzy said, but here goes:
Small island. I was there once by car, rather than cruise ship. If I did go again by cruiseship, I would definetly book a shore excursion that visited the Hemingway House. I would try to take a photo of myself at the "Southermost Point In US" marker; which looks like a 10foot milk bottle painted black, white and red. I would pickup a Keylime Pie or two. I would wander around Duval Street. If my ship did not leave until after sunset, I would try to watch it at Mallory Square. If not, the sunsets seen from onboard the ship are just as nice. I would also try to see the local street performers at Mallory Square.
I would (just like Billybuzzy) go to the Atlantis Casino and Resort. It is a giant hotel-resort seen across the chanel of water that separates Nassau from Paradise Island. The resort has the most amazing underwater aquarium that needs to been seen to believed; don't miss it.
You can get to Atlantis Casino and Resort by Water Taxi (a boat that holds allot of people and takes you across the chanell). Or, you can get there by land taxi which crosses a causway bridge connecting Nassau and Paradise Island. If by watertaxi, Just remember the path you took to get from the water taxi to the Atlantis Resort. Upon trying to return to the water taxi from the resort, I was mislead by a Bahamian man who sent me to the wrong water taxi dock (which competed with my water taxi service). Also, beware of pushy street vendors on the streets of Nassau.
CocoCay is a small party island owned by Royal Caribbean. There are a few shore excursions you might want to take: snorkeling, parasailing, wave runner rentals. However, most passengers just relaxed on the beach and ate a complementary pinic lunch.
They have waiters (from the ship) that are wondering around the beach serving drinks from the bar (which are not complementary). You can do some shopping but it was limited. You will get to shore from the ship to the island by "Tender" (which is a smaller boat similar to the water taxi). Just remember at what time the last tender makes its final trip from the island, and make sure not to miss it. That's if you plan to stay on the island until the last minute.
So, I hope this was some help. Have a nice time on your cruise.