Murray's Cheese is an institution in Greenwich Village and I have been going there my whole life at all the locations as they moved less than 100 feet at a time. The newest location across the street from the last one has much more than cheese so be prepared and bring enough money. The staff is very friendly and they will let you sample a number of different cheeses to open your horizons.
The new location is also large enough for the classes they have to teach you more the world of cheese.
Their website: http://www.murrayscheese.com/
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