The best way to see New York City, to really get a feel for the sheer beauty of such a crowded, dirty place, is from about 30 feet above the ground.
Take the J/Z Train across the Williamsburg Bridge after dark. Stand at the front of the train and watch the city fall away beneath your feet, the orange track lighting reflecting off the perfectly straight, silver rails worn to a brilliant sheen by the passage of thousands of trains just like the one you're on. Watch the cars whiz by below you and the pedestrians walk by above; three completely independent transportation systems occupying the same space, engaged in some perverse, four-dimentional (yet linear) dance; in parallel orbit, if such a thing can be said to exist.
As Manhattan passes out of your peripheral vision and the huge expanse of Brooklyn rises to meet your oncoming train, notice how perfectly still the world seems from the elevated rails and yet how in-tune with the thousands of pulses thrumming under the trestle that world seems. It's good to have a soundtrack as you do this; Ella Fitzgerald and Louis Armstrong work beautifully.
Keep this floating world in your mind when you get off your train and head down to the Brooklyn streets, to the bodegas and hustlers and such, the used condoms floating in the sewer grates. To incorporate those two worlds into one jumbled, crazy, beautiful mess is to understand New York.