Gemini is well placed for observations in December, floating high overhead in the south-east by late evening.
Castor is an easy, pretty double which resolves nicely in small scopes. A true double, the stars revolve around each other every 510 years.
Close by is NGC 2372, a faint planetary nebula that looks like a mini-dumbbell.
The Eskimo Nebula (NGC 2392), photographed so magnificently by the Hubble Space Telescope, is also known the Clown Face Nebula. Only large scopes bring out the details you would associate with a face, but it's a fun target nonetheless.
M35 (NGC 2168) is a lovely open cluster by Gemini's left foot, with a smaller, dimmer but rich companion cluster NGC 2158; physically unrelated, they just happen to lie along the same line of sight.