I can't sleep, so naturally I put in the DVD and listened to some commentary. According to screenwriter Ernest Lehman, the credits were shot on Madison Ave. The address on the building is 650 which would be CIT Financial, 650 Madison Ave, 9 stories built in 1957. Refurbished in 1987 with a 19 story addition and sadly replacing those great windows.
650 database link
edit: I don't think it is supposed to be the UN building either. In the opening scene, Cary Grant leaves his office building with his secretary and together they take a cab to the Plaza Hotel. Grant thinks it silly to take a cab two blocks, 650 is about two blocks away from the Plaza Hotel. Its the "real" George Kaplan that works at the UN, Roger Thornhill has nothing to do with the UN.
This movie seems geographically accurate. Much more so than modern movies. I saw the new Bourne movie and the shots of Chicago were not Chicago.