Amsterdam is the brightest star of a small galaxy of cities and towns that together form what the Dutch call the Randstad (Rim City), a budding megalopolis that stretches from Amsterdam to Rotterdam and contains two-thirds of the country's 16 million inhabitants.
Both the province of which Amsterdam is a part, Noord-Holland (North Holland), and the neighboring province of Zuid-Holland (South Holland) afford a number of interesting possibilities for a day outside the city -- these two provinces are the country's most important, but remember there are ten other provinces in the Netherlands.
It won't be a day in the outback, exactly, but you don't have to go far from Amsterdam to see tulips, windmills, and cheese markets. You can climb tall towers, visit interesting museums, ride a steam train, tour the world's largest harbor, and see giant locks and tiny canals. If you're historically minded, you'll want to explore sites associated with the Pilgrims (who lived in Holland for years before sailing to the New World on the Mayflower).