Did the Prophet promise his nation the conquest of New York City?

The negative answer to the posed question would unquestionably be acceptable in the first instance, simply because the Prophet died in 631 AD while the date 1624 is considered to remark the true emergence of the great city, when it was first established by the Dutch colonists under the name of New Amsterdam.

How, then, could the Prophet allude to the city, which was built about ten centuries after his death , and tell his companions that a Muslim army would invade it? Still, how could the Prophet know that the city would have had a part of it found in the sea and another one located on land? (New York City is consisted of five boroughs, four of them are found in the sea ― the Atlantic Ocean ― and the remaining one, the Bronx, is located on the mainland of the continent of North America.) Further, how could the Prophet refer indirectly to that that part of the city found in the sea would occupy three separated islands? (The boroughs of Manhattan and Staten each occupies an independent island, while the two others― Brooklyn and Queens― are both found on one island, Long Island.) And, finally, why Muslims are ignorant of this 'fact' by the moment and all their references dealing with the Prophet's speech referring that the meant city is Constantinople, now Istanbul?

In many different occasions the Prophet told his companions of future incidents[1] that would take place in the ordinary course of events, and it was during the mentioning to what seemed to be a world war between the Islamic world and Christendom that the 'conquest of the city'[2] was told. We learn from Sunna books― books into which the Prophet's speeches are compiled ― that this war will be anteceded by a peace treaty between Muslims, who will have become a world power ruled by a number of successive Caliphs, and the Christian world. Acting on that treaty, the two world powers will participate in a war against a conjoined enemy, and their allied armies will gain a decisive victory.

This very victory will cause a breach between the two world-powers, however. At the end of the battle, so we are informed, a Christian soldier will raise a Cross and will attribute the victory to the favor of it. A Muslim soldier, in objection to the act of the Christian soldier, will take off the Cross from him and will shatter it. As a consequence, a little, bloody faction will soon break out between two small groups of the conflicted soldiers, but, as the matter will somehow be settled down, the allied armies will depart the battleground in peace.

The Prophet tells us that the leaders of the Christian world will prepare treacherously for a decisive war against Muslims. Eighty Christian nations will each contribute to that war with 12 thousand soldiers, and this huge 960-thousand-strong army will secretly gather in Dabique, a wide area of meadowlands in present-day Syria. We are told also that the Muslims' command post in that future time will be in Damascus, Syria.

In the first battle of the Greatest War ― as the Prophet himself named it ― the Muslim army will meet a decisive defeat, and its members will all ignominiously flee from the battlefield. Another Muslim army will be prepared for a new battle, but this will be totally wiped out. A short passage in the available tradition indicates that some type of destructive weapons will be used against the Muslim army, for it tells us that 'no bird will fly by their side (the soldiers' corps) but will immediately fall, dead[3].' This last battle, most probably, is that one known in Biblical resources as Armageddon.

Six years later to the beginning of the Muslim-Christian world war, a seventy-thousand-strong Muslim army will start out of Medina, and this will win the war. The Prophet tells us that they will invade a city that has a part located on land and another one located in the sea, and that they will capture it without fighting. The prophet tells us of the momentous spoils the Muslim army will acquire from the city, and he tells us as well of the advance of the Muslim army from a site of that city to the other, which typically matching with the main parts of which New York City is consisted.  It is well, here, to introduce to the readers the text of the Prophet's speech to declare what I am claiming:

'Have you heard of a city that a part of it is found on land and the other part is found in the sea?' the Prophet addressed his audience. 'Seventy thousands of the Children of Isaac (Muslims of European origins[4]) will invade it. When they arrive at it, they will descend (onto its land); they will never fight by a weapon, nor will they shot a dart. They will only utter with the words, ‘No god but Allah, Allah is the Greatest,’ and thus one of its parts will fall (to them). Then they will head for its second part, and will utter for the second time with the words, ‘No god but Allah, Allah is the Greatest,’ and its second part will fall (to them). Then they will advance forward uttering for the third time with the words, ‘No god but Allah, Allah is the Greatest,’ and then it will be opened to them: they will enter it (the part located on land), and will take immense spoils... '[Imam Muslim's book of Sunna: hadith No. 2920.]

As we have seen, the city alluded to in the Prophet's speech matched with New York City in three points: (1) a city consists of a part located in the sea and another part located on land; (2) the three parts the invading forces should pass before entering the main part of the city are matching the three islands that make up the 'part found in the sea' of New York City; (3) and, finally, the momentous spoils the invaders will take from the intended city is comparable to the riches of New York as a world business center. Of no less importance, here, is the harmony between the advancements of the invading forces mentioned in the Prophet's speech and the direction wherefrom the Muslim army would be pushing to capture the city: from the eastern coast of the Atlantic, where the land of Islam is found, westward to the east coast of North America, where the army must push to Long Island, Staten and Manhattan in succession before entering the Bronx.    

In the above cited hadith (speech), the Prophet talked about a certain city, but he never named it. The old Islamic resources ― all dated back to earlier than the thirteen century ― refer to the city to be Constantinople, which had not been conquered by Muslims as yet; and the most recent resources still copying their contents without questioning. All the Prophet's companions, with one exception, shared in creating this confusion, indeed. They also thought of the mentioned city to be Constantinople, and replaced its name for the word 'city' when they narrated many other speeches concerning the Muslim-Christian world war: 'The Greatest War and the conquest of Constantinople and the emergence of the Antichrist are within the time-span of seven months[5] …'

The solitary exception was one of the Prophet's companions called Abdullah ibn Bosr, who kept the Prophet's speech without changing the word. 'There are six years between the Greatest War and the conquest of the city; and the Antichrist will emerge in the seventh year,[6]' he tells us. It is this last Prophetical Speech that indicates that the Muslim-Christian world war will last for six years.

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Resources

Imam Muslim's Book of Sunna. Imam Bukhari's Book of Sunna. Imam Ahmed's Book of Sunna. Imam Abu Dawood's Book of Sunna. Imam Ibn Majae's Book of Sunna. Imam Termithi's Book of Sunna.