If you look at the map, the 13-mile trip looks obvious, feasible and tempting. But every New Yorker carries around a mathematical map of perceived risk. The woman in Greenberg's cake shop said she wouldn't venture beyond the nineties (that is, no farther north than 99th Street). My friend Marilyn - born and bred in New York City and as hard as nails - was more adventurous, but still drew the line at 125th Street. However much you fight it, this kind of paranoia lodges itself in your mind and begins to send out little messages of panic.
But if you choose to defy the multiple warnings of potential blisters, fatigue, ostracism (Americans think you are mad to walk anywhere) and mugging, Broadway is wonderfully seductive. The rigid rectangular grid plan of Manhattan is shattered by the swagger of Broadway, which lurches haphazardly on its way from toe to tip of the island. It is longer and less disciplined than any other thoroughfare in the city, but even with the lights against you ('Don't Walk' signs are taken surprisingly seriously for a city with so much violent crime), you can complete the stroll in five hours.
Zero miles: Number One Broadway
Take a right out of Bowling Green subway station, and go north for 250 blocks; those are the only instructions you need. But before you start hiking, survey the surroundings. You are in the middle of the original European settlement, New Amsterdam, peopled by Dutch immigrants and defended not against Indians but against British troops with territorial ambitions. The Dutch had hit upon the property bargain of the millennium when they bought the island for about pounds 15, but threw it all away a century later when they swapped Manhattan with the British for what is now Surinam, a swampy corner of South America.
Behind you is Battery Park, a patch of grass filling the space between where the buildings stop and the waters of New York Bay start. Get there at dawn if you can, and sneak past a dozing nightwatchman who guards the entrance to the jetties. You can tip- toe to the end of a concrete finger, the southernmost point of Manhattan Island. If you are climatically fortunate, the Statue of Liberty will be pulling free of the morning mists that descend upon the harbour - one of the most powerful images in a city full of them.
In contrast, Number One Broadway is a bit of a disappointment: a branch of Citibank, under restoration. And at this stage the street is anything but broad, just a cramped and unprepossessing roadway.
0.3 miles: Wall Street
If Broadway seems rather modest compared with its reputation, then Wall Street is but a pathetic alley cast in the shadow of its image. There's no percentage in lingering here, so get the first couple of miles under your belt.
For its first 38 blocks, Broadway is like any other New York street: arrow-straight, pocked with potholes, home to cab drivers and panhandlers (who spend most of their energy avoiding each other). Then the road suddenly swerves to avoid colliding with 4th Avenue, and begins its merry meander through the city.
2.5 miles: Union Square
Broadway boasts half a dozen squares, but Union is the first - and last - 'proper' one. Going north, Washington, Greeley and Herald squares are all triangles, Times is a five-block-long crossroads, and Lincoln is a parallelogram.
Union Square, across which Broadway cuts diagonally, offers plenty of reasons to pause besides geometrical verity. It is the hub around which Greenwich Village and the East Village revolve (each trying to out-pose the other) and is ringed by trendy cafes. But save your appetite, and your money, for a few more blocks, since a genuine American diner is up the road at 739 Broadway.
The Famous Cozy Soup & Burger Bar does the best breakfast on the street, which is saying something for a road 250 blocks long. A miraculous pile of bacon and pancakes, eggs and syrup collides on your plate. With unlimited coffee to wash it down and ward off exhaustion, you'll still have change out of dollars 5 ( pounds 3.40).
4.2 miles: Times Square
Theatres are the one thing Broadway lacks as it winds through the Theater District. Almost all the theatres are in nearby side-streets rather than on Broadway itself, which has cinemas. Hence it is easier to obtain tickets for Pillows of Lust or Hot Oriental Orgy than for a first-rate show. The sort of characters who hustle along this traffic-choked strip are likely to create the first rumbles of anxiety in the long- distance walker.
5.1 miles: Columbus Circle
Christopher Columbus never got nearer than 1,000 miles to Manhattan; the man credited with the discovery of America never, in fact, set foot in it. But the US has adopted him as its own, and his statue duly presides over the heart of the nation's biggest city.
If you have started the journey without a map, you can pick one up from the New York Convention and Visitors Bureau here. Be warned, however, that the advice given in official publications can be misleadingly optimistic about the attitude of New Yorkers to visitors. The bureau doesn't quite advise that 'waiters and taxi drivers prefer a polite 'thank you' to a tip', but it is not far off this level of misinformation.
6.2 miles: 80th Street
Sid, the neighbourhood newspaper vendor, is an environmentalist. He sells newspapers by the ounce rather than the pound from his paper stand outside Zabar's Delicatessen.
Sid never pays for his stock. Each Sunday, locals buy the heavyweight New York Times and immediately offload good chunks of it at Sid's stall. He collects and recycles them within minutes, charging a modest 25c (17p) for each section rather than the dollars 2 ( pounds 1.35) you pay for the works.
His line in patter is priceless: 'Wanna good cry? Get a business section,' he yells to passers-by. He will also do a special deal on a subway map - which he picks up for nothing at the local station.
Two blocks north, at 82nd Street, the cafe at the new Barnes & Noble bookshop is the city's latest pick-up joint. If you succeed, take your new friend to the movies: Loew's Multiplex is diagonally across Broadway.
7.7 miles: 110th Street
If the hike could be regarded as a military campaign, then this is still the phoney war. Columbia University lends neo-Classical pretension to this stretch and attracts an entertaining class of panhandler. 'I'm a loser, pal - I dropped fifty grand at Atlantic City.'
8.4 miles: 125th Street, Harlem
The frontier. Beyond here, they warn, you are leaving your rights behind. The rules are different. The street itself is subtitled Dr Martin Luther King Boulevard, and forms a valley: Broadway takes a dip while the accompanying subway line emerges from the slope to be borne across the valley. The sight would be impressive were you not staring anxiously at those around you.
8.9 miles: 135th Street, Harlem
Anyone who is 6ft 2in tall (as I am) knows it can be disconcerting to encounter people significantly taller - especially if there are three of them bearing rapidly down upon you and particularly if you are in unknown territory that everyone has warned you about. My eyes leapt around, searching vainly for help or escape. When the gaze of the tallest was about six inches away the unthinkable happened. He yelled, 'Boo]'.
I jumped, he chuckled, his companions roared with laughter. They melted past me and guffawed away down Broadway. I tried to see the funny side of it, too; but at 138th Street I came across the aftermath of a drive-by shooting. Fearing a walk-by mugging, I leapt on to a bus and trembled in comfort for a couple of miles.
9.9 miles: 155th Street
The transition to solidly Hispanic territory coincides with the best views of the journey. Manhattan is an Indian word for 'many hills', but only this far north do you find what would be rolling countryside were there any greenery left. On one side is the arrogant span of the George Washington Bridge, bearing Interstate 80 away across the Hudson River and the continent to San Francisco. On the other, the surface of the Harlem River reflects the dramatic desolation of the South Bronx.
You are in a parallel world to the planet of plenty at the other end of the island. The language is Spanish, the street furniture could be in Havana or Bogota. The pace of life is genuinely slower here, and the people more considerate. The newspaper kiosk at the corner of 155th Street is run by a blind man, who operates entirely on trust - a risky enterprise. All American banknotes are the same size, so if you say you've given him a dollars 10 bill, he gives change accordingly. And he's still firmly in business.
11.5 miles: Fort Tryon Park
The tension melts away as you brush against the first park for miles. Fort Tryon Park isn't just a good, green place to calm down, it also contains New York City's most extraordinary museum. The Cloisters is the sort of folly that only a family of billionaires could bring to fruition; when the Rockefellers heard the word 'culture', they reached for the family fortune.
The Metropolitan Museum's collection of medieval art, as it has now become, consists mainly of four Pyrenean monasteries shipped over early this century by John D Rockefeller. They were reassembled close to the top of Manhattan Island, filled with other European treasures and choreographed into an immensely pleasing, if a trifle unsettling, ensemble.
12.5 miles: 213th Street
You're definitely back in the world you began in. The first health food shop sprouted at 205th Street, and here the Irish Eyes pub signifies a return to the comforting probabilities of New York - that you probably won't get mugged, and you'll probably be able to find a decent pint.
13 miles: 9th Avenue and Broadway Bridge
By this stage, Broadway is easily the dominant thoroughfare in Manhattan. A few yards short of the top of the island, 9th Avenue, having slunk intermittently alongside for a few miles, abandons the struggle to keep up. Broadway, the artery, presses on northwards across the bridge named for it. The street has saved its most perfect panorama to the very end: the Harlem River gouges a deep channel to the east, the Hudson River shimmers handsomely, and, behind you, Manhattan rises gracefully. It seems scarcely credible that this is the same city whose skyline carves a vast, jagged silhouette across the horizon farther south. And New Yorkers will hardly believe that you've been for a Sunday stroll, and survived.
(Photograph and map omitted)