More NYC…
There’s a really, really old song, like about 100 years old, about the Bowery and why the singer’ll never go there again.
More L.A.
I don’t know who sang this or what the title was, but there was a song from about 12 years ago where the female singer says,
All I want to do is to just have fun
I gotta feeling, I’m not the only one
All I want to do is to just have fun
Until the sun comes up over Santa Monica Boulevard.
L.A.:
Hollywood Babylon - The Misfits
Santa Monica - Everclear
Disneyland - Eyes
Seattle:
Viva Sea-Tac - Robyn Hitchcock
My Possee’s on Broadway - Sir Mix a Lot
U2 - Angel of Harlem
Billy Joel - You May be Right (reference to the Bedford - Stuyversyn section of Brooklyn)
NWA - Straight Outa Compton (I believe Compton is a suburb or section of LA)
London
“Oxford St., W1” by The Television Personalities
“Bar Italia” by Pulp (It’s around the corner, in Soho, where other broken people go)
“The Boy With the Arab Strap” by Belle and Sebastian mentions Old Compton St
San Francisco
“Piazza, New York Catcher” by Belle and Sebastian mentions the Tenderloin
Not a city, but
Minnesota
“Buck Hill” by The Replacements
Texas
“Possum Kingdom” by The Toadies
I’ll think of more once I look at my music collection.
An oldie: MacArthur Park. (Park in downtown Los Angeles.)
If we’re going to go for any song that includes a London location in its lyrics, we could be here all night 
Athens, Georgia:
The B-52’s “Deadbeat Club” says, “Let’s go crash that party down in Normaltown tonight”
The B-52’s “Love Shack” says, “Headin’ down the Atlanta Highway, lookin’ for a love getaway”
San Francisco and Berkeley, California:
Soul Coughing’s “White Girls” starts with, “White Girl, Market at Van Ness.” and that verse ends with “Inclines and wires, Telegraph Avenue.”
Cyprus Avenue in *Belfast ** is mentioned in at least two of Van Morrison’s songs, Cyprus Avenue * and Madame George from Astral Weeks.
One more for London: Willesden to Cricklewood (Joe Strummer & the Mescaleros)
By my, admittedly very unscientific, count - where song title meets the OP and both artist and city are obvious - the tally so far stands thus:
“Bad Bad Leroy Brown” by Jim Croce (South Side of Chicago)
It’s part of Baltimore. My sister lives there! But Ms. Orton was apparently referring to London, which also has a Mt. Zion and a St. Jude Street.
Have we had Auckland yet?
By Crowded House
Smokey Robinson: “There is a rose in Spanish Harlem…”
Glenn Campbell, Broadway, “Rhinestone Cowboy”
The song Oregon Hill , by the Cowboy Junkies, is about a very distinct neighborhood right here in Richmond, VA.
New York: Simon & Garfunkel: The 59th Bridge Street Song (Feelin’ Groovy)
Santa Monica is it’s own city. It is part of the L.A. Metropolitan area, but it is not part of the City of Los Angeles.
San Francisco: “Russian Hill” by Jellyfish.
London: “Towers of London” by XTC.
Wiltshire, near Swindon: “Chalkhills and Children” by XTC references the Iron Age Uffington Chalkhorse there.
Auckland, NZ: “One Tree Hill” by U2
Another about Chicago:
Lincoln Park Pirates
Moon Over Bourbon Street by Sting.
California:
“Going to California,” Led Zeppelin
“California Dreamin’,” The Mamas and the Papas
“California Sun,” Rancid
“Under the Bridge,” Red Hot Chili Peppers
Nevada:
“Viva Las Vegas,” Elvis
“Friend of the Devil,” The Grateful Dead (mentions Reno)
Oklahoma:
“Oklahoma!,” Oklahoma!, the musical
Omaha:
“Omaha,” Counting Crows