New York City has been called "the center of the world." The Big Apple has big influence. Even the fonts used in the logos for the New Yorker and in the tourist slogan, "I love NY," are popular. Here you can find resources and download links for fonts, and more, in a New York minute!
New York Themed Fonts
Fontspace.com has a collection of free fonts associated with NYC. There's one based on the New Yorker Magazine front cover, called "Cygnet." If you're looking for something reminiscent of classic Broadway, there's one named "Broadbay." Other original sets in this category, including one that mimics the LED display of a subway ticker, and one in which the capital letters are accompanied by cartoon "big apples" while the lower case features taxis. Here's where you can browse all of their New York Fonts.
I Love New York
This iconic logo was created in 1977 by graphic designer Milton Glaser, who is also known for designing the DC Comics logo, as well as co-founding New York Magazine. If you're wondering what font is used in the I love NY logo, it has been identified as "Amercian Typewriter." There are several variations on this font, including bold, medium, light, and condensed, so it's a judgment call regarding which version is the closest approximation.
Here is one location where you can download the free American Typewriter font.
If you want a decent match of the heart used in the logo, a free font called I Love Romance contains one that looks very similar.
New York Yankees Font And Other Styles
If you want to mimic other NY symbols, you'll generally need to spend some money or use what's available in the derivative style. For instance, a good, high-quality font comparable with the New York Yankees team logo, called Metroscript, is available, but for purchase only. It's not all that cheap, but it will do the job for emulating not only the New York Yankees font, but the Mets as well. The logo is based on a script type of font, such as Shelley Script, which is downloadable as freeware, but not particularly reminiscent of the Yankees.
The New York Times logo is another one that you can get close to by using an Old English-based font. The Helvetica font is used by the Metropolitan Transportation Authority, so if you want the typeface used in the subway system, you can buy the very same one.
Manhattan File Transfer
There are a couple of commercial fonts bearing the name "Manhattan." One of these has the letter look of Art Deco, and another is a collection of silhouetted symbols, mostly of traced photos of pedestrians, with a few cars, buses, and a fire hydrant thrown in for good measure.
To expand on the busy street aspect of the city, some additional resources include free road sign dingbats, and an additional set of dingbats that feature skyscrapers and city skylines.
So now you know what font is used in the I love NY logo, and you've got a reasonable facsimile for the New York Yankees font, and you've got a number of additional New York themes to make use of. This should help you "make a brand new start of it!"
For more free font options, check out Finding and Using Free Fonts for Windows.