Having been to St. Bart's two times, I would stay nowhere else by the Eden Rock hotel.
Two minutes from the airport, great mostly private beach, terrific rooms.
Yes, it is one of the most expensive hotels on the island, but worth every dollar. Great restaurants, great rooms. If you can afford it, try a rock suite....one of the seven suites actually built on the rock.
Even if you stay elsewhere, go one night for dinner....great food...great atmosphere.