Barbara De Kegel attempts to get to grips with the city that never sleeps, as she learns New York is more than just ManhattanNew York City: home of bagels, men in suits, and the world’s largest melting pot. It’s a city which should not be underestimated. If you happen to get off the subway too early, you may find yourself in an area unmarked on the eight tourist maps you grabbed from the airport. It's only in dubious Brooklyn neighborhoods, where the local Wi-Fi networks are named after hard drugs and female body parts, that visitors will truly realise New York isn't just Manhattan. That there are places where the streets are desolate, the buildings abandoned, the walls graffiti clad, and the trees missing. Even the greatest cities on earth have their hardships, but few of the people on the street seem to have gotten that memo. They say hello and carry yoga matts and are more than willing to help out a lost soul, fresh off the boat.For a proper first introduction to the city, wander onto Williamsburg Bridge, amidst power-walking locals, preferably from the Brooklyn side. You’ll see Manhattan with fresh eyes, not noticing, from the distance, the havoc, road works, and bulging sidewalks you’re accustomed to expect. All you see is an impossibly vast, dense expanse of skyscrapers, standing in silence: it is surreal.Williamsburg Bridge itself is a stunning piece of architecture that links the two most hipster New York neighborhoods. This bridge lacks the iconography and hordes of tourists its cousin, Brooklyn Bridge, claims, but instead offers character and a great walking path, above the occasional rattling of a J-train.The New York subway is a tourist’s dream. It can get you everywhere your guide book could mention, and for a much more reasonable fare than London’s Tube. However, if you do happen to have a couple of days, and you're an avid walker, taste the fruits of America's rich immigrant history by foot, and discover places such as Borough Park, home to an impressive Orthodox Jewish community.While Chinatown is the most well-known neighborhood with a strong, omnipresent culture, it certainly isn't the only one. Between the kosher supermarkets, and identically dressed and coifed locals of Borough Park, you'll feel immensely out of place, in an intriguing sort of way.Downtown Brooklyn boasts Prospect Park, brought to you by the creators of Central Park. It features a vast rolling meadow, popular with readers from the neighboring colossal Brooklyn Library, as well as school groups, gossipy sunbathers and self-proclaimed park enthusiasts.Cross jogging in Central Park off your to-do list and gaze at the views from around the Jacqueline Kennedy-Onassis Reservoir. Take a ferry to Ellis Island, home of US immigration, from Battery Park on the southern tip of Manhattan, and listen to young buskers in Washington Square Park, the garden of New York University.However, the most unique and worthwhile of the New York parks is the old elevated railroad track, turned greenway, called the High Line. Stretching from the Meatpacking District to Chelsea, the Line offers views over the city, as well as the Hudson River. In some places the old tracks have been incorporated into the new design, and the wild vegetation flanking the path is an ode to the Line's previous abandonment. The first section of the High Line was only opened in 2009, after years of local advocacy for the Line's preservation.Also deserving of a visit is the recently opened 9/11 Memorial, at the heart of the World Trade Center site, which is now towering over the New York skyline. In the midst of a tree covered pavilion, in the exact location the Twin Towers used to stand, there are now two immense square-shaped holes with waterfalls thundering down from all four sides. It's a stunning way to preserve the footprints left by 9/11.The best deal in town is undoubtedly the Staten Island Ferry. Running from the Whitehall Terminal, South Ferry to Staten Island, 24 hours a day, this bright orange ferry provides spectacular views of Lower Manhattan, New York Bay, and the Statue of Liberty. Aside from the views, a break from the smog of the city for an hour of wind and sea air warrants the trip alone.Not quite so cheap are the $100 Broadway tickets. However, several shows do offer comparatively low-priced tickets through lotteries or special box offices. These aren't advertised, and are somewhat of a well-kept secret. Every show day, a guy with a bucket sits on a ledge outside of the New World Stages from 6 to 6:30pm. If you walk up to him you can enter your name in a lottery for 25 dollar front-row tickets to RENT. During the week only a handful of people show up, and there's a good chance you'll be sitting in your prized seat one and a half hours later. Due to it being Off Broadway and in a small theater, the show is intimate and personal; you feel as if you're in the story rather than watching it.A couple of days in New York may lead you to conclude that an intricate, compartmentalised toolbox would be a better analogy than a melting pot. New York's neighborhoods can almost be marked off with lines. Sometimes you turn a corner, and all at once the buildings are a different style, the people are of a different ethnicity, and you don't understand anything anyone is saying. And that's the most striking thing about this city: it is a thousand radically different places.