Best Value in town: Eden Rembrandt Square Hotel. Apart from being a newish hotel, in one of the best areas of Amsterdam (especially at New Year!) offering all creature comforts and very comfortable beds, it is not easy to find free internet connection in Amsterdam in many places.
There are two desktops in the lobby and WiFi network. You can easily connect with your own laptop as there is an LAN connection in the room free of charge. However with the red light district only a 7 Euro tram ride away, the Internet was not required this trip!
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