SXM is a great place for these ages - lots of wonderful beaches and activities. If they are interested in watersports, parasailing, etc., Orient Beach is a great location, plus a beautiful beach with lots of bars, restaurants, beach chairs, music and people watching. (It's my teen girls favorite beach to spend a day.) Yes, because it is on the French side of the island, you will find people more casual about sunbathing topless and one end of the beach is a naturist resort. I've been taking my kids there for more than ten years, and for us and many others it's not an issue. But be sure you tell your teens not to be rude gawkers, though.
Your daughter and friend would likely enjoy a visit to the Butterfly farm, which is located near Orient. Try to go on a day with fewer cruise ships, so you don't arrive just as a bus load of cruisers does.
An activity our teens loved was the Rhino Riders. They are like a jetski built into a dingy. Fun for jumping waves, and you go on an excursion with a guide to a place to snorkel and just to ride the waves. You need to be 16 to drive your own, if I recall correctly. You'll find info on activities on Jeff Berger's website about SXM -
http://www.everythingstmaarten.com/
A great resource for info on jewelry stores, restaurants, etc. is the St. Marten bulletin board on traveltalkonline. It's at
http://www.traveltalkonline.com/forums/postlist.php?Cat=0&Board=stmartin
If you read through old posts you'll find lots of discussions about where to buy jewelry, etc., The board has many regular posters who each have their own favorite rental car company, jewelry store, restaurant, etc., so postings asking about these topics can become quite heated! We've had good luck at DK Gems, a favorite of many, located on Main Street in Philipsburg but have bought at other places, too. Also avoid jewelry shopping on Main Street when multiple cruise ships are in port - too many people to be able to negotiate well. The traveltalkonline bulletin board has a link that shows which ships are in port each day, so check it shortly before your departure.
One place to encounter locals is at the "lolos," the small locally owned food stands. Many are in the main street of Grand Case, a city on the French side, although there are several around the island. Again, you'll find past discussions about lolos on the traveltalkonline bulletin board.
About your teens having a car - I don't know where you live, but I would never give my teens the same freedom to go off independently on SXM as I do in our MN suburb and even into Minneapolis. Crime does occur on the island, and it's too easy for teens to end up in the wrong place. And like another poster said, driving is crazy and SXM is not be somewhere a teen should be behind the wheel. I'd look for ways to give the teens some space, like while on a trip to a beach or during the day in Philipsburg, but not give them too wide a rein otherwise.
One restaurant they would like is Pineapple Petes. It has pool tables to enjoy while you're waiting and gets high marks for good food and service at fair prices.