The Quadrantids is one of the best meteor showers of the year, but its best will last for just a few hours.
It's also best seen from the northern hemisphere, unfortunately.
The Quadrantids' radiant is high in the northern sky, making them all but invisible for southern hemisphere observers.
For those interested, the name Quadrantids is derived from a now-obsolete constellation named Quadrans Muralis which was incorporated into Boötes during the International Astronomical Union's inaugural meeting in Rome in May 1922 when the official set of 88 constellations was defined.
At best we in the south might see a few meteors low in the northern sky - anyone further south than latitude 51 deg will see nothing.
The best time for viewing will be in the early hours of the morning of January 3rd for viewers in North America and (assuming it lasts long enough) the early hours of January 4th in eastern Asia (China, Japan, Korea etc).
Of course the other problem will be the waning moon right in the middle of things.
Also, for those interested, NASA will be running a live stream from a camera at the Marshall Space Flight Centre in Huntsville Alabama. Note that the camera image is only available when the site is dark.