NYC has a wealth of major hotels. Mid-town hotels include:  The Plaza (Central Park West and 59th Street), NY Hilton (1335 Avenue of the Americas), Holiday Inn (440 W. 57th Street), Grand Hyatt (Park Avenue at Grand Central Station), Millennium Broadway (145 W. 44th Street), Milford Plaza (270 West 45th Street).

Columbia has negotiated rates with a number of hotels both in mid-town and elsewhere (westside, eastside) for Columbia employees, affiliates and guests.  (http://procurement.columbia.edu/purchasing/contracts/hotelRates.pdf)

For accommodations near Columbia University's main campus, a few subway stops from the Medical Center campus, call Landmark Guest Rooms (affiliated with Union Theological Seminary and Columbia University) at 212.280.1313 or Teachers College, Columbia University at 212.678.3235 (ask for Guest Housing). 

The NYC Tourism website offers a wealth of information on the city and its attractions. (http://www.nycvisit.com/home/index.cfm)