In NY, people in THE bronx, (always with an article) go down town, and every one in the other boro's (usually the long spelling in NY) goes to the city when coming into manhattan.
And like London, natives take the IRT, BMT, and IND subwaylines. These are designations from the original companies that built the subways. The companies went belly up more than 50 years ago, but "Real NY's" still use the designations. Out of towners call them red line, blue line. Sophisticated transplants have learn to refer only to the numbers and letters (take the A train, or take the number 7 line-).
NY maps indicate there is an Avenue of the Americas in NY, but no one calls it that, its 6th Avenue. the name was changed sometime before my birth --so immediately pre or post WWII. It was still 6th Avenue in the 30's, when the el (elevated railroad) was torn down, and sold as scrap metal to Japan. (local story is the 6th avenue el sunk the pacific fleet- the scrap from the el being used by Japan to make the bombs.)
I live in Queens-- so i have been denegrated as one of "the bridge and tunnel croud"
An other curiousity is, if you look at a map, you might think Queens is part of Long Island. but in NY, polictics is stronger than geography, so both Brooklyn and Queen are not considered part of Long Island. So I come from Queens, (named for queen Charlotte) not from Long Island. my early childhood was spent in The Bronx, so i still head downtown each morning to work, while most of my nieghbors go to the city.
