The monuments and museums, the bridges and the tunnels, the Brooklyn bodegas and the Fifth Avenue boutiques: Over the years LIFE’s photographers explored every pulsing corner of New York, the great city the magazine always called its headquarters. From the countless images of the Big Apple in the archives, LIFE.com now presents classic black-and-white photos that show off the architecture, the spirit, the culture — images that are a testament to a city that, through darkness and in light, remains one of a kind. Pictured: the Statue of Liberty, as captured by Andreas Feininger in 1943.