Depending on time of day you arrive I would start with a quick road trip around the island in a rental car to get the feel of the island. That can be done very easily in a couple of hours. Beach days I would recommend would be a day at Orient, day at Mullet and a day at Pinel or some other beach destination you came across in your travels the previous days.
You can also incorporate a stop in Grand Case at one of the LoLo's on the way back from one of the beaches or go there for lunch beforehand depending on what beach you go to and what route you've taken.
I would not take the time to go to Anguilla with having such a short stay. To much to see and do in St Maarten with so little time.