I have done two Regent cruises over New Years (one was also over Christmas). Bare minimum of kids and I had a fantastic time. When all the drinks and bubbly are free; it makes for a wonderful experience. Regent Seven Seas Navigator has a 15 night cruise this year that covers both Christmas and New Year's; if I wasn't cruising in January, I would jump on it. Here is the link to the cruise on the Regent website. A good TA should be able to get you 5% below these posted prices.
Luxury Cruise Vacations from Regent Seven Seas Cruises
Also, Regent is (elegant) casual every night; no reason to pack any fancy clothes.