I'll take the obvious route and suggest Tori Amos's "Scarlett's Walk," with "I Can't See New York" in particular and ones like "Amber Waves" as well.

The Pogues, Fairytale of New York and Thousands are Sailing

I love Luka Bloom's "Dreams in America" (I don't have a non-iTunes version of this one). And "Mona Lisas and Mad Hatters" (I like the Indigo Girls' bootleg best, but then that's probably pretty shocking. For a road trip through the U.S., there's always Melissa Etheridge with Baby You Can Sleep While I Drive. And for the cheesy awful regional selection, Dan Fogelberg with Run for the Roses! Kentucky Derby is May 6th, after all. :-D

The classic would be Frank Sinatra, "New York, New York."

"The Boy from New York City" by Manhattan Transfer (among others)
"Big Man on Mulberry Street" by Billy Joel
"The 59th Street Bridge Song (Feelin' Groovy)" by Simon & Garfunkel
"Strawberry Fields" by the Beatles
"Harlem Shuffle" by the Rolling Stones

Broadway-related songs would be good, too: "42nd Street," "Lullaby of Broadway," "On Broadway."

I have a big soft spot for They Might Be Giants, "New York City" (I understand it's actually a cover of a punkier song by a group called Cub).

Dar Williams' "Southern California wants to be Western New York"

http://www.amazon.com/gp/product/B000002ZCC/002-3510148-5252865?v=glance&n=5174

Sufjan Stevens, "Chicago"

Trust me on this one, the second verse is about New York

http://www.amazon.com/gp/product/B0009R1T7M/qid=1144796827/sr=2-1/ref=pd_bbs_b_2_1/002-3510148-5252865?s=music&v=glance&n=5174

Ace Frehley - Back in the New York Groove

Oh, also. If you still have the very old 1970s MP3 2 disc set I gave you several years back, you have the Ace Frehley song, too.

"Chelsea Morning" by Joni Mitchell
"Miami 2017 (Seen The Lights Go Out on Broadway)" by Billy Joel
"New York Minute" by Don Henley
"New York, New York" by Grandmaster Flash and the Furious Five (not the same as the Frank Sinatra/Liza Minelli song. But you probably knew that. *g*)
"No Sleep Til Brooklyn" and "An Open Letter to NYC" by the Beastie Boys
"On Broadway" by the Drifters

America in general: "America" by Simon and Garfunkel

General America: Neil Diamond, "America"

But I can't really say I *love* it. ;-D

I do love Ray Charles' version of "America the Beautiful", though.

Do you need these to be cheerful songs at all?

If not, well there's always Leonard Cohen. I'm not sure how well "First We Take Manhattan" is suited to your purpose; other than the namecheck in the title it could be anywhere.

"Famous Blue Raincoat" mentions a chilly New York in the lyric though.

Well, for America, there's the entire Springsteen oeuvre. *g* I'd go with "Rising" and "My City in Ruins" and "My Hometown".

If you can find it, "Seeds" is fantastic--it's a live track from the mid-80s. Not happy, but so vivid and angry. Great song. Also, "Jackson Cage". "Cadillac Ranch". "State Trooper". "Light of Day" (another live-only track). I'll stop now.

Steve Earl, Copperhead Road. Chrissie Hynde's song about Ohio (memfault).

Happy stuff:
John Hiatt, Buffalo River Home. Indigo Girls, Southland in the Springtime. Kate Wolf, Golden Hills of California. Dave Carter and Tracy Grammar, Highway 80. Any version of Route 66 you can find.

I third "Fairytale of New York." Everyone else seems to have this under control but I'll take this opportunity to say "hi" and wave merrily in your direction.

How very nice of you to make mix CDs for travel! Here are a few songs I'm guessing others haven't mentioned.

London:
Derren Raser Band, "Streets of London" (download available here)

New York:
Matt Pond PA, "Brooklyn Stars"
weaklazyliar, "Empress of New York" (download available here)