The area known as Silicon Alley is in Manhattan. Like the more famous Californian Silicon Valley from which is takes its name, Silicon Alley is so called because it is home to a high number of internet and new media businesses.
The original centre of this area was on the Broadway corridor - mainly the region of the Flatiron district, Soho and Tribeca (triangle below Canal Street). However, there is now so much computer based business in New York that the term is used to refer to this business in New York generally, rather than to a geographical location.
There are no alleys in New York, so the name is a bit of a joke to rhyme with Valley.

There is a neighbourhood in Brooklyn called Dumbo, which is sometimes also called Silicon Alley because it contains a number of technology and other modern companies.
You can read more about new businesses in New York here.