Tom Clancy's Splinter Cell: Chaos Theory
Chaos Theory's story spans everywhere from Japan to Panama, but there's a particularly exciting level around the middle that takes place in NYC.
We don't want to spoil it for you, but Sam Fisher has to infiltrate the HQ of a private military corporation owned and operated by an old friend. It's exciting stuff, though it doesn't exactly play off the city's strengths for Fisher to be skulking around in the shadows. Hence its high place on the list.