If you blink, you might miss the Quadrantids Meteor Shower. It peaks in the hours right before dawn Jan. 3, with a maximum number of meteors per hour of about 80.
The Quadrantids come from an asteroid called 2003 EH1, just as the Geminids did in early December. Meteor showers usually are named based on the constellations where they originate. Quadrans Muralis (mural quadrant) between Bootes and Draco.
The meteor shower is expected to "last only a few hours,"according to NASA.com. That means you should look for it in the the night of Jan. 2-3, not the night of Jan. 3-4. The moon will set after midnight, so the best time to view the meteors will be between then and sunrise at about 7:50 a.m.
If there is cloud cover in Apple Valley or Rosemount on that night, you can watch a Ustream feed of the meteor shower on Jan. 2-4 on NASA.com.
Obviously, you'll have more luck catching the shooting stars if you're in a place not polluted by light.
In Apple Valley, that makes your best bet Lebanon Hills Park, which boasts plenty of wide open and dark spaces.