Red light district is the name of ANY prostitution district in ANY town, not just the one in Amsterdam. Locally the one you are referring to is known as "De Wallen".
The stadium name you are looking for is spelled slightly different: http://www.johancruijffarena.nl/ , not saying that "Cruyff" should be wrong, but maybe you could include the correct spelling as well.
I'm not sure I've heard anyone actually living in Amsterdam refer to it as the "Venice of the North". According to Wikipedia, that particular epithet seems to have been applied to at least 38 other cities in various countries - probably by people on TripAdvisor with too much time on their hands.
A better answer to the question would be "Mokum" - the actual nickname applied by Amsterdammers to their city themselves (and a name that should be easily spottable by anyone visiting the city with half an eyelid open and an enquiring mind, which admittedly isn't the case for a lot of visitors after about half an hour...)
The stadium name you are looking for is spelled slightly different: http://www.johancruijffarena.nl/ , not saying that "Cruyff" should be wrong, but maybe you could include the correct spelling as well.
A better answer to the question would be "Mokum" - the actual nickname applied by Amsterdammers to their city themselves (and a name that should be easily spottable by anyone visiting the city with half an eyelid open and an enquiring mind, which admittedly isn't the case for a lot of visitors after about half an hour...)