Almost any place in the Netherlands can be reached within 3 hours or less of rail travel due to the small size of the country and excellent rail network. It is possible to see most of the country via day trips from Amsterdam. Here are some of the possibilities:
Alkmaar - historic town with its cheese market.
Delft - well-known for its typical blue and white ceramics.
Den Bosch - typical city for the Southern Netherlands, goes crazy during carnival.
Den Haag (The Hague) - political heart of the country, Madurodam, and Scheveningen, the most popular beach of the country.
Enkhuizen - interesting village with the Zuiderzee Museum, that shows how people used to live with the persistent danger of the sea.
Haarlem – the closest of the historic cities.
Hilversum - wealthy town known for it’s magnificent town hall, also offers interesting cycling tours through forests and the heath.
Hoorn - historic port that played a large role in the history of the Dutch East India Company (VOC).
Keukenhof - a seasonal attraction in the Spring, these enormous flower fields are popular among travellers.
Kinderdijk - this authentic network of windmills shows the typical Dutch countryside at its best.
Muiden – formerly a small port at the mouth of the Vecht river, it boasts the Muiderslot, the best-known castle of the country.
Rotterdam – has a history of rivalry with Amsterdam, and a completely different atmosphere with modern architecture.
Utrecht – Historic town that has a less-ambitious canal system.
Volendam - once a fishing village, it is now the most commercialised tourist destination in the Netherlands (Edam and Marken are nearby and more authentic).
Zandvoort - closest beach resort.
Zuid - Kennemerland National Park – a unique national park made of dunes formed over the centuries.
Around Amsterdam, there are dozens of museums worth visiting. Here is a list of some museums that are an easy day trip from Amsterdam by train: