A few years ago we took a look at the Central Park ducks as part of a DIY Holden Caulfield walking tour. Now, following J.D. Salinger's death, CityRoom has created a nice little interactive map if you want to stop by all of the places the author long left behind him when he moved to New Hampshire. (Another photo tour can be found here.)
But if you want to retrace the steps of Salinger himself, and not just one of his fictional creations, then Bowery Boys and Inside the Apple are your guides. With our typewriter ribbon changed, we'll now attempt to break it down into some useful bullet points:

Myron Arms and a young Salinger
- Salinger was born on January 1st, 1919 at the Nursery and Child's Hospital on West 61st Street and Amsterdam (now known as New York Presbyterian Hospital and Weill Cornell Medical Center).
- He first lived at 3681 Broadway at 153rd Street, across from the Trinity Church cemetery.
- After that, he hopped around other Upper West Side abodes as his family moved from place to place (three times between his birth and 1928).
- By his teens, he was at 1133 Park Avenue, at 91st Street, a home that is said to be what he based the Caulfield's on.
- At one point the family landed at the Myron Arms at 221 West 82nd Street (pictured), which is still standing.
As for school, he attended the McBurney School on West 64th Street (though he flunked out) and also went to New York University for a year, prior to Columbia University—which he didn't graduate from but during his time there he did publish his first short story. (The New Yorker hints to a lot of Salinger in their next issue, and provides links to his stories published in the mag here.) And if you're interested in where Salinger had been hiding out all this time, his neighbor has opened up about what it's been like to live next to the famous recluse.