Fight Night - S3-E7
Plot hole: A large part of Nick's plotline revolves around the discovery that the couple's stolen ring has a fake diamond switched out for the real one. But the ring was left as collateral for a very expensive necklace for the woman to wear that night. There is no way that a jewelery store would accept a ring for collateral without appraising the ring's/stone's value first. And in that inspection, they would have discovered the switch and not accepted it.
Answer: The episode on CSI:NY was called "Love Runs Cold" and first aired on October 4, 2006 (Season 3, Episode 3) and involves the investigation of a model found stabbed to death by an ice dagger.
OneHappyHusky