New York cruise destinations change according to the season. This is also true for Bayonne, NJ (also known as Cape Liberty) which is just across the river from Manhattan.
Bermuda is a spring / summer / fall destination. 7 nights is the most common length, but 5 and 6 night options are becoming more common. These cruises often stay 1 or 2 nights docked in Bermuda. These overnight stops are a relatively rare treat, especially among the mainstream cruise lines.
Canada + New England is a summer / fall destination. A typical 7 night cruise that returns to New York won’t get much further north than Halifax but a one-way will normally end in Quebec City or Montreal.
Bahamas sailings are usually 7-10 nights long and are the most year-round of the options.
Caribbean itineraries are rarer, but when available, are 10+ nights long and mostly found in the winter.
In addition to end-of-season repositioning cruises, New York is also a common starting point for World cruises and one end of a semi-regular transatlantic sailing to England (Southampton, ~90 mins from London).