I was scanning a list of best restaurants in the U.S. and noticed that a large number of them are shown as being located in “New York, New York.” Three of them, though, are listed as “Brooklyn, New York.” Last time I checked, Brooklyn was one of the five boroughs in New York City. Shouldn’t Brooklyn restaurants also be listed as “New York, New York”? Is there some secret code here that “New York, New York” really means Manhattan?
Pretty much always been that way, especially for Brooklyn.
Recall, in Arsenic and Old Lace, the opening text differentiated between ‘Brooklyn’ and ‘The United States proper’.
Whenever I hear “New York, New York”, I immediately think of Staten Island. 
Brooklyn is part of NYC but it used to be a separate city. Granted, that ended in 1898 but some habits die hard. It still had a fairly strong individual identity in living memory and arguably, even today (think The Brooklyn Dodgers baseball team). What you are seeing is a remnant of that. I personally think only of Manhattan when I see the reference New York, NY.
I once rented a car to drive from Sacramento to the Bay area. The counter lady asked if I was going to be taking out out of the country. I said I might be crossing through Berkeley.
She wrote it down.
I most remember it from the intro of Welcome Back Kotter. Kind of confused me as a kid, as I had never thought of Brooklyn as its own city.
Despite being a single city, you address letters to the various parts of New York City in different ways:
Brooklyn, the Quebec of NYC. 
Brooklyn is in the late stages of a hipster renaissance, so it is the “cool” place to be. So the restaurants that are not just in NYC, but actually in Brooklyn probably want to emphasize that fact.
I should also add that, yes, when I see “New York, NY,” I assume Manhattan. I’m not sure I’ve seen a Queens or Brooklyn address given as New York, NY, but I am not from that area. I have addressed many things out there, and usually it’s something like Richmond Hill, NY (which is part of Queens, and therefore part of New York City) or Jamaica, NY (another part of Queens), etc. The only friends I for whom I have addresses that are New York, NY, live in Manhattan, so I’ve grown to assume the default assumption is New York, NY, is Manhattan.
It’s kind of interesting, though, and maybe New Yorkers can help me out. I see Queens addresses often given by neighborhood name (i.e. Richmond Hill, NY; Astoria, NY; Jamaica, NY). However Brooklyn neighborhoods seem to be usually addressed as Brooklyn, NY, instead of Park Slope, NY, or Williamsburg, NY. Is my observation correct, or just selective memory of addresses I’ve seen?
Nothing much but ZIP codes has mattered for quite a while, anyway. Street address or box number and zip code will get a letter anywhere in the US. Town and even state are a holdover/convenience for manual sorting.
The municipal government of the City of New York covers all five borough-counties—Manhattan/New York Co., Brooklyn/Kings Co., Queens/Queens Co., The Bronx / Bronx Co., and Staten Island/Richmond Co.
But the postal address “New York, New York” is pretty much just Manhattan. The postal address for Brooklyn and the Bronx are Brooklyn, New York, and The Bronx, New York (IIRC), and Queens is divided up into numerous postal areas mostly named for pre-merger localities, like Flushing.
This can create significant ambiguity in searching depending on whether the relevant databases are using jurisdictional boundaries, postal districts, user-chosen designations or some combination of such.
Oh, I’m an idiot. It’s right there in Wendell Wagner’s post. Consider this answered.
Good summary in link by Wendell Wagner though it’s a little more convoluted in Queens than that. Many addresses there are ‘[old town=modern neighborhood name], NY’, but sometimes the old town name refers to a larger region of Queens than the modern neighborhood name you use to say where you live. For example I used to live in Fresh Meadows, an old name of part of the pre-Revolutionary War town of Flushing. Some addresses in the adjacent modern neighborhoods of Utopia and Auburndale also have postal addresses Fresh Meadows, NY. Others have addresses Flushing, NY. And some addresses in Queens are ‘Queens, NY’, ie [Borough], NY, like all (AFAIK) of Brooklyn, Staten Island and Bronx addresses. Only in Manhattan do you use a county name which is different from the borough name in the postal address: New York, NY.
Back in the early '70s I lived in Brooklyn Hts. for a few years. I always gave my address as Brooklyn, NY. Never Brooklyn Hts. or New York, NY.
If someone asked me where I lived, though, I’d say “Brooklyn Heights,” just as when living in Manhattan, I’d say “Chelsea” or “Soho.” But these would never be used as an actual address.
But Queens is different.
Yeah, I noticed later that Wendell’s post actually has a link explaining the quirky addressing customs. Interesting read.
I suspect that most cities have similar quirks. London certainly does. A londoner, talking to a non Londoner would say he came from London. To another local, he might say Wandsworth or Isle of Dogs. It’s also possible that he might work in The City; an enclave in London a bit like The Vatican in Rome.
Large towns and cities have swallowed innumerable villages and small town over the centuries. Some will be clearly defined boroughs but others might just be a small area within a borough or across boundaries. London has Paddington and Soho as examples of this.
Whatever the law says about the 5 boroughs, I have noticed that when I used to fill out internet address forms, with my old address in the Bronx, that they would not accept NY, <zipcode> NY. The city, the first “NY”, had to be Bronx to be accepted. As if for some reason the boroughs of New York City had become independent. After all, they are only counties officially.