Prices skyrocket the first day of the new year, which is 28 Jan 2017. They stay high for about a week or so, until everyone (especially the Mainland crowd) goes back to work. This will likely be around Feb 3/4/5.

You can find excellent deals (both hotels and flights!) up until the night before the new year. By the way, the deserted streets that evening are quite the experience - you could film a sequel to I am Legend that night.