I've been on Celebrity to Bermuda and the Caribbean before as a teen and of liked it. But I wouldn't expect many teens for the Mediterranean.
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?