https://www.bookwitty.com/text/a-tour-of-literary-new-york-city/5820a10050cef744229e966d suggests six places to visit.
To that list I would add two other hotels:
The Hotel Chelsea (at 222 West 23rd St.) had several writers as residents and guests: Thomas Wolfe, Eugene O’Neill, O. Henry, Jack Kerouac, and Dylan Thomas.
The Plaza Hotel (Fifth Avenue and Central Park South) hosted Truman Capote, Dashiell Hammett, F. Scott and Zelda Fitzgerald, Carson McCullers, and Dorothy Parker.
There are also a number of bars for bibliophiles:
Chumley’s (86 Bedford St.) had John Steinbeck, Theodore Dreiser, Willa Cather, Edna St. Vincent Millay and Eugene O’Neill as patrons.
McSorley’s Old Ale House (15 East Seventh St.) was immortalized by e. e. cummings, and Frank McCourt bestowed to the bar a signed copy of his memoir Angela’s Ashes.
Pete’s Tavern (129 East 18th St.) has a sign indicating O. Henry’s favourite table where he penned “The Gift of the Magi” in 1905.
White Horse Tavern (567 Hudson St.) was a favourite of Dylan Thomas who apparently once downed a reported 18 shots of whiskey at the tavern. Jack Kerouac mentioned the bar in his novel Desolation Angels.
While in New York, you might want to take a literary tour. There’s the Bohemian and Beat Poets of Greenwich Village tour (http://levysuniqueny.com/tours/bohemians-and-beats-of-greenwich-village-literary-tour/) and the Greenwich Village Literary Pub Crawl (http://www.literarypubcrawl.com/), among others.
If you love browsing through bookstores, here’s a list of bookstores in New York City: http://bookriot.com/2017/03/22/my-quest-to-visit-every-bookstore-in-nyc/.