We visited two main towns of the island - Philipsburg on the Dutch side and Marigot on the French side. We did some shopping in both places, had lunch in La Source in Marigot, made a short trip to Baie Rouge, and had dinner at http://lechanteclair.com in Marigot.
La Source is a small restaurant on one of the back streets near Marina Royale. The food there is so good that we went there again on our way back from Anguilla.
Le Chanteclair is right on the Marina Royale and the food there was great too. Ol'ka particularly liked the French Onion Soup.