Lincoln Center for the Performing Arts
Lincoln Center is a collection of performing arts institutions located on the Upper West Side, near where Broadway awkwardly intersects with Amsterdam Avenue. In the 1950s, the immigrant neighborhood of San Juan Hill was razed to make way for the complex. (Interestingly, the film of West Side Story was shot in the neighborhood shortly before its destruction.)
Columbia students receive few specific discounts at its many venues, although all New York college students are typically welcome to $10 performances of the City Opera on some nights.
To get there, take the 1 train to the 66th Street-Lincoln Center subway station.
Julliard, with which Columbia has a formal affiliation, is nearby and is vaguely part of the center. Fordham has an adjacent campus as well. Columbia was also planning a physical location along the Hudson River near here, called "Columbia Prime", on land owned by Donald Trump, but PrezBo nixed those plans and chose to build a new campus in Manhattanville instead.