Cooper Union (no 's) is a college in the East Village. No connection to Lincoln Center, which is uptown and on the West Side, except that Lincoln gave a famous speech there in 1860. Two things to keep in mind when you consider accomodations: New York City (Manhattan) has a really fine (OK, a bit shabby, but still competent) public transportation system, so you don't have to be terribly worried about finding a hotel in one part of the core city or another, and it is a great woaking city. Both facts take the pressure off of finding a hotel in the "perfect" neighborhood.
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