We stayed at the Eden Roc hotel, and that's all you need. The hotel is fantastic (here are a couple of pictures), although pricey, but you have the best beach on the island, the best service, the best food, and the best view. It's French based, they prefer Euros, so again, it's pricey.
You can walk less than 5 minutes to the town of St. Jean, and there are plenty of less expensive places to eat, and shop. The island is small, about 8 square miles around, so don't go for too much action, but there's enough. Nicki Beach hotel is right next door, and there is a pretty good downtown (Gustavia) with restaraunts and shopping as well, and bars.