We took a cabbie tour of the island. It was nice. Ended up going to Orient Beach for a beach day and drinks in some of the dozens of Tiki Hut type bars. One word of caution, Orient Beach is a French dominated area and clothing optional is the norm. Some of those people needed ironing.
My husband and I were on the Carnival Glory in March and booked a trip to the Divi Little Bay Resort. They served lunch and we were able to relax on the beach for the entire day. I understand that you can use the resort's swimming pools if you don't like swimming in the ocean. There are also shops on the resort grounds. Just make sure that you rent a beach umbrella as the sun can become merciless after a couple of hours. The umbrellas rent for $5 for the day but are well worth it.
lots of stuff - some of which has already been suggested:
take a taxi tour - you can see most of the island in about 2 hours
rent a car - but be aware on days when lots of cruiseships are in, traffic can be heavy
shopping - Philipsburg has some good jewelry stores, Marigot has some excellent quality French stuff and incredibly yummy French goodies at bakeries
beach - my favorite thing to do. Orient Beach is long, pretty, lots of restaurants,lots to do (jet skis, water trampoline etc) (Note you will see some nude people - most however will have bathing suits on), Le Galion - shallow, gentle water - good for kids, Dawn beach - very pretty and casual, decent snorkeling when it's not rough, Maho Beach - the place to go to see the big planes land and takeoff but don't get sand blasted and so many others
Lord Shieffeld - tallship day cruise
Butterfly Pavilion - near Le Galion beach
st Martin park (small Zoo)( - near Philipsburg)
we rented a car and drove to orient. it's probably 10 minutes from pier to orient in the morning. probably 20 in the afternoon when traffic is heavier. took us longer than this since the roads don't have numbers. hard to find way, but we didn't mind since we got to see a lot of nice sights along the way.