As far as other things to take in:

Parotte Ville - a parrot sanctuary where the birds will eat out of a cup given to you and will light on your head, shoulders, etc. A simply wonderful experience!

The Zoo - so much fun feeding the goats out of your hand!

Tijon - also lots of fun making your own perfume/scent (not just for ladies!)

Loterie Farm - zip lining, cabanas around a beautiful pool, restaurant/bar "in the trees"

Passaat - do not miss a sail on the Passaat; they offer half-day sails, sunset sails, and dinner sails. Others will recommend other sailing experiences, but this is my favorite.

While the island has 37 beaches, I am partial to a few on the French side:

Anse Marcel - a beautiful beach with gentle water and a beach bar with wonderful food

Friar's Bay Beach / Friar's Bay Beach Club

Petite Plage - beach associated with Grand Case Beach Club

La Playa - restaurant and bar on Orient Beach run by Bruno Lemoine

Dreams - great beach bar on Nettle Bay. The beach isn't that great, but this is another wonderful food establishment run by Bruno Lemoine

This should give you a start! Have a great trip!