When you are in Amsterdam you will be faced with a city full of things to do. If you only have a day or two you may just want to see the city -- there is so much to do there that you'd need a few weeks to see it all. Everyone will find plenty to fit their tastes, from shopping to museums to bars and cafes. Of course there are coffeeshops and the Red Light District, but that is not unique to Amsterdam.
If you have more time in Amsterdam you should get out and see more of Holland -- the Netherlands offers much more. A short train trip away is the city of Haarlem and the beach town of Zandfoort. Further out are the popular Dutch towns Leiden and Delft. Of course Rotterdam, the Hague, and Utrecht all have their positive points as far as big cities go. The coastal countryside of Zeeland and the friendly culture of Maastricht wait for your visit.
The populated, industrialized areas around Amsterdam are collectively called the Randstad, or Rim / Ring City. This includes Amsterdam, Utrecht, Rotterdam and Den Haag (the Hague). Amsterdam is the tourism capital -- Rotterdam, by contrast, is a tremendously commercial city.
The Rotterdam port is the largest in Europe. Before WWII Rotterdam was a more popular place for tourism. After Rotterdam was bombed, it never was rebuilt in the old style like other bombed cities (Munich). Amsterdam has evolved into the shiny symbol of Holland, while Rotterdam bears down and does the dirty work. If you ever drive on the bridges over Rotterdam harbor, you will see what I mean -- there is an amazing concentration of heavy industy there.
Utrecht is a major road transportation hub, with most of the trucks entering Holland going through Utrecht. From Utrecht, you can easily get anywhere in Holland or Europe by train. Utrecht is worth a day's visit - it has all the charm of any Dutch city, plus a special charm of it's own. The pathways that run at water level along the river/canal are nice, and the Dom is a prominent feature.
The Hague is not only the Dutch political capital, it's also one of three European Union capitals (the others in Luxembourg and Brussels). Amsterdam does not have a monopoly on museums - both the Hague and Rotterdam contain prominent collections of Dutch Master's painting and other works. Call museums ahead of time in the winter months to see if they are open or being remodeled. Even when a museum is open it may have some of the collection in storage.