They call Times Square the Crossroads of the World. If that is a fair description of the intersection of Broadway and 42nd Street, then it is reasonable for the many millions of residents to conclude that the totality of New York City with its five boroughs, 322 square miles of territory, 175 languages on its frenzied streets, concentration of corporate Goliaths and neck-cricking skyline ranks as the capital of the Americas. Today's calculation proves as much, though the city is beaten by the narrowest of margins by London for the title of capital of the world.

Yet visitors whose first priority in other major cities is posing in front of grandiloquent political edifices will be disappointed. New York is not a capital. Not of the United States and not even of New York State. That honour rests with Albany, a much greyer place up the Hudson River, and one that few tourists bother with. Even City Hall in lower Manhattan, housing the offices of Mayor Michael Bloomberg, is disappointing when you consider the mighty city he governs. Possibly an outing to the Stock Exchange off Wall Street will include a glance at the nearby Federal Hall. That is where the first US President, George Washington, was sworn into office. (Yes, New York was the original US capital but only until 1790.)

One structure that might save the day is Le Corbusier's United Nations tower on the East River. Diplomatically, therefore, this is the world's capital, never mind if the UN has never really lived up to its early promise. And the building is still wondrously elegant, until you pay to take the tour inside, when you will see how decrepit it has become. A $1.8bn (900m) revamp is supposed to start next year.

Landmarks, however, New York is not short of. Putting your shopping destinations to one side Bloomingdale's, certainly, and probably Macy's on Herald Square, the SoHo boutiques, and the bargain Century 21 near Ground Zero the list of must-sees is longer than a Philly cheesesteak sandwich.

You will probably count among them the ice rink at Rockefeller Center, Central Park, a harbour tour to catch the Statue of Liberty and also the Ellis Island Museum, which recalls the tides of huddled immigrants that first populated the city and helps put its growth into a historical and demographic context.

Do all that and still you have only scratched the surface. There are, of course, the skyscrapers. Building tall has long been New York's way of advertising its pre-eminence and commercial clout to America and the rest of the world. Before long you will be able to watch the new Freedom Tower take shape where the doomed Twin Towers once stood.

Nor is New York to be outdone by anyone when it comes to cultural offerings. London's West End and Manhattan's Broadway are in competition for top spot in theatre rankings. The recent stagehands' strike on the Great White Way (as Broadway is known) reminded many of us of everything that is happening on off-Broadway stages too. There are roughly 200 theatre companies occupying venues the length and of breadth of Manhattan and beyond.

The rivalry between New York and London never seems to end, in fact. Who wins between the Tate Modern and MoMA? Between the National Gallery and the Metropolitan Museum of Art? It extends into sports too. You have Wimbledon, we have Flushing Meadows. In America, however, only New York boasts two national league baseball teams. Both, meanwhile the Yankees in the Bronx and the Mets in Queens are busy building brand-new stadiums. New York competed to host the 2012 Olympics too, by the way.

The two cities at either end of the world's busiest long-haul air route have traditionally vied to be the world's financial command centre, too. New York still boasts the two largest bourses globally, the New York Stock Exchange and the Nasdaq, and has no real rivals to the title in the Americas, but has been feeling the heat of late from a resurgent City of London.

For New Yorkers, it is a clich to say that their city is almost a country unto itself, separate from the rest of the United States. The size of its economy alone means that it would come in at 17th among the world's nations. Yet, as a melting pot, it is the quintessence of America. You know it from the multiple tongues heard on the subways, the multitudes of foreign-language newspapers on sale, and just by looking about you. With 36 per cent born outside the United States, New Yorkers really are world citizens.

New York beat the world in terms of flights, market capitalisation of the stock exchanges and as the location for the headquarters of global corporations