I've been twice during the first week of January. In 2005, the crowds were very slight. I waited until about 10 days after the new year. In 2008, I went on Jan 5 and the crowds were heavier but still better than any other time of year in my opinion.
It depends on what day of the week New Year's falls. If there's a weekend shortly afterward, people will probably hang out until the weekend is over and head back on Sunday.
That's all speculation on my part, I don't know what historically happens. My advice is to wait just a little longer and go mid January. Just watch out for the marathoners.