42nd Street
Lullabye of Broadway
Walk on the Wild Side – Lou Reed
Mona Lisas and Mad Hatters – Elton John
New York City – John Lennon
There aren’t any words to the song (that I know of), but when I hear “Rhapsody in Blue” I think of Woody Allen’s movie, Manhattan (and United Airlines, damn commercialism).
Get New York: Songs of the City, which is all about songs about New York (and the boroughs!), from the 1700s to today. Excellent, entetaining book, too.
Rockaway Beach–the Ramones
Sweet Jane by Lou Reed always seems very New Yorkish to me, though I’m not sure why. The entire Lou Reed/Velvet Underground catalog is probably full of New York songs. (Take a Walk on the Wild Side, of course)
And I beg you not to use New York State of Mind. It was so overused before 9/11, and after 9/11…yeesh!
Silver Bells.
West End Avenue–from “The Magic Show.” By Stephen Schwartz pre-Wicked.
“New York, New York” (not that one, a different one) by Nina Hagen
It’s, um, unique. Also foreign.
One more, “Song for Myla Goldberg” by the Decemberists
I got distracted by Robot Arm mentioning that fabolous “New York City” song and some actual office work, but here’s a short list and a post that actually contibutes to this thread:
- “Bostich” by Yello: no New York references that I know of, but big cityish.
- DJ Hells “NY Muscle” LP - it’s German (Lyrics are english and some tracks are instrumentals). No obvious NY refences though.
- “An open Letter to NYC” by the Beastie Boys
- “New York USA” by Serge Gainsbourg
Andrew Lloyd Webber’s “Tell Me on a Sunday” later to become the “song” part of Song & Dance is about an English girl who moves to NYC. Lots of NYC songs, with one called “I Love New York” appearing 3-4 times. The best version is the Marti Webb original “Tell Me on a Sunday” and the 2CD live “Song & Dance,” along with Bernadette Peter’s Broadway “Song & Dance.” The recent Denise Van Outen London revival is okay.
For more information, check out www.eur.com/musicals
there’s “new york, new york” by ryan adams. it’s aight.
nas’ “new york state of mind” is a classic.
digable planet’s “borough check” is great, if you don’t mind a slightly gritty take on brooklyn.
brooklyn, brooklyn big borough of dreams
but everything in brooklyn aint always what it seems,
you might get jacked if you come from out of town
we’re down by law and that’s word…
actually, the whole blowout domb record by digable planets seems to mention brooklyn in every song.
“blowout COMB”, that is.
Chelsea Morning and Tin Angel - Joni Mitchell.
59th Street Bridge Song - Simon & Garfunkel.
The Camera Eye - Rush. The entire first verse is about Manhattan.
“In the City,” Eagles (closing credits theme to The Warriors- how could you not think NYC!) 
“Looking for Love on Broadway,” James Taylor
“Good Evening, Mr. Waldheim,” Lou Reed (from New York, which someone already mentioned. Always sounded to me like the true-blue native New Yorker’s “New York” song. . . barbed pre- 9/11 references to Rudy Guiliani and other politicos)
“Diamonds on the Soles of her Shoes,” Paul Simon (that wonderful verse “She said honey take me dancing but they /Ended up out sleeping in a doorway/Near the bodegas and the lights on upper Broadway”)
Famous Blue Raincoat - Leonard Cohen.
It’s Over (I Am Legendary, You Are Not) by Hungry Wives badmouths every trendy place in New York.
Ryan Adams - My Blue Manhattan is fantastic even though I hate New York.
I hope I’m not duplicating - George Benson’s On Broadway.
They say the neon lights are bright, on Broadway…
Harry Nilsson wrote a song that has been covered by a few artists, including Sinead O’Connor (as heard on the soundtrack of You’ve Got Mail): I Guess the Lord must be in New York City.
IMHO, your presentation can’t be considered complete without a segment showing joyous Yankees piling on one another in celebration of a World Series win, complete with the classic version of New York, New York. Love 'em or hate 'em-The Yankees are synonymous with New York 
Another not mentioned: Beastie Boys-No Sleep 'Til Brooklyn
Good luck with your project.
“Hot child, summer in the city, back of my neck getting hot and gritty…”
I hear that, and in a flash I am back in the summer of 78, working the night shift at the local ER. 3 in the morning, no business, docs are sleeping in the oncall room, the triage nurse has her head down on her desk, the radio room lights are dark…
Man! It’s amazing how a song can take you back to a specific time and place…