I think you will get a workout from the fully loaded wallet you will have to bring, because there is no such thing as an inexpensive St Barths trip. There is plenty to do, and restaurants abound. Shopping is excellent, and spotting is very cool, if somewhat limited. Make sure you rent a minimoke if they haven't yet been banned, and do a day trip on a sailboat. Scuba diving is decent and there is horseback riding as well as plenty of trails to hike.
The Karl Gustav is the nicest hotel according to the literati, but I personally like Filao Beach Hotel for the comfort and relative value. It ain't cheap but its still lower cost than many others on the island. There are plenty of villas to rent by the weekend or week, if that floats your boat. Email me if you are serious and want to find a good place.
Is my Pan Am ticket to the moon still good?