Since I don't live in NYC I can't address how the neighborhoods are today, but here's some historical areas no one mentioned:

1. The homes Al Capone grew up in. He was born in Navy Street then moved to 69 Park Avenue, then three different places on Garfield, all in Brooklyn.
2. The area around the downtown Manhattan courthouse is where the Five Points Gang was. It's also not far from the World Trade Center.
3. There are three useful books for Mob-related tours of NYC (actually there are more, but these two are the easiest to obtain):
http://www.amazon.com/Goodfellas-Guide-N...k+city+mob+tour
http://www.amazon.com/Manhattan-Mafia-Gu...mafia+guidebook
http://www.amazon.com/Gangland-New-York-...A4Q0EVWD68S828H

There's also an app:
http://www.amazon.com/Mafia-Walking-Tour...k+city+mob+tour

4. The first Mafia-related killing in NYC was near the Cooper Union building at 30 Cooper Square, near downtown. It was in 1888.

5. If you go to Little Italy, make sure to hit Elizabeth Street. That's where the early New York Mafia was situated (for the most part)

6. If you want see where the Bonannos started, it was in the Williamsburg section of Brooklyn around 5th and Roebling, which is now mostly Hasidic Jewish and hipster.

7. The Morellos started out around 106th Street in Italian Harlem, but you probably don't want to go there.