Willemstad is both a big city and a small town. Residents live in the hills surrounding Schottegat, and much of the city is sprawling and rather mundane. But this all changes radically in the old town. Here the island’s colonial Dutch heritage sets a genteel tone amid markets, museums and even a nascent cafe culture. Wandering the Unesco World Heritage–recognized old town and absorbing its rhythms can occupy a couple of days.