Peak season for Hawaii is March-April, June-August and holiday sailings. Though some consider June-August too hot, summer months will always be high season because that's when families go on vacation. Though January is cool and wet, it is a great time for whale watching.
Obviously, rates are lower during low season -- late November, February (except for Valentine's cruises) and May. If you want to sail over the Christmas or New Year's holidays, you'll pay peak rates and will need to book your cruise six months to a year in advance.
The only year-round week-long cruises out of Honolulu are offered by Norwegian Cruise Line, which dedicates its Pride of America to that itinerary. Carnival offers two April and two fall sailings, and Royal Caribbean generally has ships in Hawaii once in April and once in September.
Many cruise lines -- from small, luxury vessels to megaships with all the bells and whistles -- visit Hawaiian ports during the year, as part of a longer cruise or repositioning to other destinations/itineraries.
A Christmas cruise of Hawaii on NCL's Pride of America makes a wonderful family experience, complete with nighttime volcanic lights, instead of decorative house lights, and Santa decked out in a Hawaiian shirt bringing gifts to children on board.