I'm guessing you're first formal night will be the night after your first fun day at sea, and your second formal night will be the night before your last fun day at sea.
Past Cruises (all except one from NYC)
Carnival Triumph to Canada: August 1999
Carnival Victory to Canada: July 2000
Celebrity Zenith to Bermuda: July 2001 AND July 2002
Celebrity Galaxy to Caribbean (from Baltimore): July 2003
Voyager of the Seas to Caribbean: July 2004
Crown Princess to Caribbean: July 2006
Carnival Victory to Canada: August 2007
Carnival Miracle to Caribbean: May 2008
Staten Island Ferry, I mean what else in NYC is free?