1. A well-known prison located in eastern New York State, along the Hudson river. The base for such phrases as 'up the river' (as it is located up the Hudson river from NYC) and 'the big house' (because it's a... big... place.).
2. A popular nickname for Ossining, NY, the town in which Sing Sing prison is located.
"Hells no! I'm not gonna do that! I don't want to end up in Sing Sing!"