The first quarter moon should set just after midnight leaving dark skies for what could be a good show. Best viewing will be just after midnight from a dark location far away from city lights.
Also, check out the conjunction of Jupiter and Saturn, which will appear as if they are a single body!
The Ursids is a minor meteor shower producing about 5-10 meteors per hour. It is produced by dust grains left behind by comet Tuttle, which was first discovered in 1790. The shower runs annually from December 17-25. It peaks this year on the the night of the 21st and morning of the 22nd. Meteors will radiate from the constellation Ursa Minor, but can appear anywhere in the sky.