Definitely good information here and most I would recommend myself. Some other note worthy things to do or try:
If you like outdoors and athletic activities, I'd recommend trying some of the zip lining on the French side. It's a pretty fun obstacle course then zip lining from tree to tree.
French side has some great restaurants ranging in pricing.
I'm not sure if you're into clubbing and casinos. There are quite a few over there to have a good time at.
Depending on how long you stay and your budget, I'd recommend you taking a day trip to Anguilla and/or St. Bart's. Anguilla is a really nice remote island with better beaches than St. Maarten. You feel like you're in a private island away from civilization, pretty nice a peaceful. If you fly to St. Bart's it's quite an adventure to say the least. It's a pretty short flight in a small plane and landing on the short strip is pretty cool. The island itself is very upscale and expensive. You feel like you're in Europe, except in the Caribbean.