The five boroughs of New York City are broken down into hundreds of neighborhoods (seriously) like Red Hook, the Upper East/West Sides, and Greenwich Village. Some neighborhoods are cleverly named pertaining to their locations such as Tribeca (Triangle Below Canal St), Nolita (North of Little Italy), and Dumbo (Down Under the Manhattan Bridge Overpass).
Some neighborhood nicknames haven't quite caught on. Recently, there has been a push for "FiDi" - AKA, the Financial District, and "SpaHa"... Spanish Harlem. There's even MiMa... which is Midtown Manhattan, of course ;)
Soho is short for "South of Houston", but unofficially, Soho means fashion and shopping! Stores such as Uniqlo, Madewell, Lush, and new addition Aritzia take up residence in the old cast iron buildings. Is there nail polish to be found in Soho? You bet! Shop department store lines at Bloomingdales, check out what Forever 21 has to offer, and stop by MAC to see their latest collection. Topshop also released a line of makeup, including many vibrant nail polish shades.
For more about the neighborhoods of NYC, check out New York Magazine's handy dandy neighborhood guide. But like everything in New York City, the neighborhoods are ever-evolving :)