Day trip
Most of the Netherlands can be reached in a day trip from Amsterdam. There are dozens of small traditional villages, medieval cities, beach towns and windmills to visit just a short bus, train or even bike ride from Amsterdam. The following are a few suggestions:
Hoge Veluwe Park and the Kröller-Müller Museum: An hour southwest of Amsterdam, this large national park is a unique combination of nature, culture and art. It's a good place to see wild deer, boars and birds. There are free bikes and lots of walking trails. The park is also home to the Kröller-Müller Museum, a world-class modern art collection, surrounded by Europe's largest sculpture garden.
Den Haag (The Hague): The Netherlands' third largest city is certainly a destination in its own right, but it can easily be visited from Amsterdam as it's only about an hour away. There are excellent museums and a totally different feel from Amsterdam, making it a good place to experience Dutch culture outside of the big city.
Delft: Between Den Haag and Rotterdam, Delft is a charming little town—very characteristic of Dutch towns of its size—but with two big draws: the famous Delftware factories cranking out blue and white ceramics for hundreds of years and Johannes Vermeer, the famous painter who was born and died here.
Tulips: In the springtime, of course, blooming fields of tulips are a big attraction and there are plenty of places to see them close to Amsterdam. Look for maps of bike routes through the fields between Haarlem and Leiden.