My advice always is to arrive at the port the day or night before. Particularly if you're coming from the northeast in winter, it's "better safe than sorry" to my mind. New England can be hit by snow storm in March, and a little extra wiggle room can be nice. It also insures you against mechanical breakdown of your car getting in the way of your cruise.
You can take advantage of your extra day and go to New York City. Or, if you come down the night before, you will know you can wake up on cruise day with peace of mind and start your cruise relaxed.