I traveled this new years eve' to Amsterdam and was surprise to see the difference between this city and the majority of european capitals. Surprise in a good way.
First of all, dont be mistaken by the legend of coffe shops and red light district. There is more in Amsterdam then those things. First of all, i reccomend u to go in summer, becouse if u are not used to low temperatures u will froze in winter becouse of the windy freezing athmosphere, and it would be a pity not to visit the open air attractions, like their parks, their squares and the busy streets.
The public transportation i found expensive, so if u are in a group of 4 its better to take a taxi then the tram.
Once u are in the central part of the city just take a map and u can walk by feet all around (from china town to red light district, from red light district to dam square, from dam sqare on kalverstraat to rembrandtplain or to flowermarket and leidsestraat and so on)
RembrandtPlein, Museum Plein, Flower Market, Dam Square, Leidseplein and Leidsestraat and ok, once ur there u should also see the China Town and Red Light District.
What's really great:
Everything from the people kindness and the positive athmosphere.
The canals, boatcruise
A beer maybe?
Try to get accomodation in the centre (maybe book a few months before u go) otherways u will pay a lot for taxi/tram.
If u dont get a central position i reccomend Bastion Hotels
Should try Escape club & lounge in RembrandtPlein, especially if ur there on New Years EVe
Liedsestraat and Kalverstraat for shopping and busy traffic