If you just want a fun day at the beach.... no suggestions needed. Just get yourself a chair and relax in the sun. It is one of the best days you will have on your cruise as it is SOOO RELAXING. Most people tend to stop at the beach right after you get off the tenders.... but if you continue to walk to the tip of the penisula or to the side facing out into the ocean you will find alot less people on the beach.
There are wave runners which can be rented as part of a tour... and also some water activities (snorkeling, water slide, iceberg, and a small water park) which you can buy tickets. To lay on beach costs nothing... unless you want a floating lounger.
We went to Labadee last year and we went kayaking.....it was pretty cool....you just have to make sure to wear plenty of sunscreen and rest the day before (because you'll give your arms a workout). but, i think, next time i'm just going to lay on the beach and take it super easy! :-)