A lot depends on your interests, of course, but here are some ideas for you to think about.
In Nassau--visit Paradise Island and have a friendly person take a picture of the two of you in front of the famous Atlantis Hotel.
On Coco Cay. This is a "ship's private island" to which you will most likely be tendered. It's nice but you tender over and back with a crowd and there are not many secluded spots on the beach. You might want to go over early to visit, because it is a pretty beach, then, if you want romantic time alone, take one of the early tenders back--you will have most of the ship to yourselves.
On Key West. A visit to Margarittaville is a must if you like anything "Buffet." You can get a margaritta and try conch fritters with hot sauce in the restaurant and shop for tee-shirts, caps, and other island gear in the shop next door. You might also want to visit the shop (in town) that sells jewelry, coins, and other treasure recovered by deep sea treasure hunters--or you can just ogle all those goodies and pretend you are bucaneers chortling over your haul.
On the ship: Be on deck for the sail away from each port with a favorite cocktail. Dress up for the formal night if there is one. Seriously, a pretty evening dress and tuxedo won't look out of place. Arrange for a formal portrait or line up for one of the more quickly posed, but still very nice photos taken on formal night. Have the wait staff sing "Happy Anniversary to You," one night at dinner. Book a massage for both of you. You'll feel great. Do something you would not do at home--whether it's singing at karoke night or having fun pool side with a silly game like who can stuff the most tennis balls into their bathing suit--let yourself go and have a good time!
We took our first cruise for our honeymooon and are now at 17 cruises and counting. I wish you the same success.
It is very romantic :naughty