If you are staying on the island for multiple days, don't be afraid to explore. Minibuses, vans with "bus" license plates, pick up all over town. Rides are $1.50 and are payable when you get off. The minibuses go all over the dutch side and the french side. A very cheap and simple way to get around. Rent a car; it is very simple to get around and people are friendly. You can get around the island in about 1 and a half hours total time. Be warned, Sint Maarten drivers are aggressive and streets are narrow. It is not uncommon for a driver to swing out from a parking space into heavy traffic. Don't leave anything of value in the car.
Shopping is duty free on the island. Front street is lined with shops selling every trinket and piece of jewelry you could desire. Several marquee brands, like Cartier, have outposts here. For a better deal check out the market in the middle of town. Prices start out at about the same as all the other tourist shops but haggling is allowed and encouraged. Just be willing to walk away and prices plummet, especially if you're the only one looking.
Lolos pop up all around Sint Maarten after the sun goes down and are a cheap and delicious way to get a little taste of the Caribbean. Be sure to try the BBQed chicken and Johnny cakes. Johnnies at pondfill 34 is fantastic. Chicken is $3 and Johnny cakes are 50 cents. (see same topic for Saint Martin)
Try local drinks such as Guavaberry Liqueur which is sold in the authentic store at the head of the main streets in the heart of the town of Philipsburg.
(see same topic for Saint Martin)