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The Village Voice is a free weekly newspaper in New York City, United States featuring investigative articles, analysis of current affairs and culture, arts reviews and events listings for New York City. It is also distributed throughout the United States on a pay basis. Source: en.wikipedia.org

The only daily in New York devoted exclusively to Brooklyn.

The Staten Island Advance is a daily newspaper published in the borough of Staten Island in New York City. It is the only daily newspaper published in the borough and the largest by circulation, covering news of local and community interest in the borough, including borough politics.
The Advance was created in 1886 by printer John J. Crawford and businessman James C. Kennedy as the Richmond County Advance. The name was changed to the Daily Advance before the current name. When the Advance began there were nine competing daily newspapers in Staten Island. The circulation of the Advance surpassed its early competitors, and the circulation grew from 4,500 in 1910, to over 80,000 by the mid 1990s. Source

The Daily News of New York City is the fifth most-widely circulated daily newspaper in the United States with a daily circulation of 703,137, as of March 30, 2008. The first U.S. daily printed in tabloid form, it was founded in 1919, and as of 2007 is owned and run by Mortimer Zuckerman. It has won ten Pulitzer Prizes.
The News carried the slogan "New York's Picture Newspaper" from 1920 to 1991, for its emphasis on photographs, and a camera has been part of the newspaper's logo from day one. The paper's later slogan, developed from a 1985 ad campaign, is "New York's Hometown Newspaper", while another has been "The Eyes, the Ears, the Honest Voice of New York"). The Daily News continues to include large and prominent photographs, for news, entertainment and sports, as well as intense city news coverage, celebrity gossip, classified ads, comics, a sports section, and an opinion section. Source

Barron’s is an American financial magazine known for its market-moving stories. With new content available every week in print and every business day online, Barron’s provides readers with a comprehensive review of the market’s recent activity coupled with in-depth, sophisticated reports on what’s likely to happen in the market in the days and weeks to come. Source

The New York Post is the 13th-oldest newspaper published in the United States and generally acknowledged as the oldest to have been published continually as a daily, although -- like most other papers -- its publication has been interrupted by labor actions.[2] Since 1993, it has been owned by media mogul Rupert Murdoch's News Corporation, which had owned it previously from 1976 to 1988. It is the 6th-largest newspaper in the U.S. by circulation.[3] Its editorial offices are located at 1211 Avenue of the Americas, in New York City, New York. Source

The Wall Street Journal (WSJ) is an English-language international daily newspaper published by Dow Jones & Company, a division of News Corporation, in New York City, with Asian and European editions. As of 2007, It has a worldwide daily circulation of more than 2 million, with approximately 931,000 paying online subscribers. It was the largest-circulation newspaper in the United States until November 2003, when it was surpassed by USA Today. Its main rival is the London-based Financial Times, which also publishes several international editions.
The Journal newspaper primarily covers U.S. and international business and financial news and issues—the paper's name comes from Wall Street, the street in New York City that is the heart of the financial district. It has been printed continuously since being founded July 8, 1889, by Charles Dow, Edward Jones, and Charles Bergstresser. The newspaper has won the Pulitzer Prize thirty-three times[3], including 2007 prizes for backdated stock options and for the adverse impact of China's booming economy.

The Queens Tribune is a free weekly newspaper founded as the monthly Flushing Tribune in February 1970 by Gary Ackerman. It is based in Fresh Meadows. The Tribune is a member of the New York Press Association.
Every month, the newspaper issues a special edition that focuses on a given topic. Recurring examples include the Best of Queens, Arts & Culture, Blue Book, Gay Pride, and Community Characters editions. Source

The Haitian Times is a weekly newspaper for Haitians living in the wider area of New York City, New York, United States. The newspaper is printed in English, as opposed to French or Haitian Creole, and is based in Brooklyn. According to the website of the newspaper, the total weekly circulation is 30,000, Brooklyn circulation is 18,000, Queens, New York City circulation is 6,000, Long Island circulation is 4,000, New Jersey circulation is 1,000, and circulation beoynd greater metropolitan New York City is 1,000. Source