If you like nature, you can head west out to Red Rock. There's a 7 mile scenic drive and lots of hiking (December may not be the best time, I suppose).
Skiing and snowboarding are available in December on Mt Charleston, a short drive north of Vegas.
http://www.skilasvegas.com/winter/index.htmlOther random things:
Tour of the Neon Museum
See the Ethel M Chocolate Factory
Tons of shopping, of course
Spend the day in a spa
There's a zoo, but I wouldn't recommend it
The Bellagio has an art gallery
Take a trip to the Hoover Dam
Madame Tussauds is in the Venetian
I think there may be a new Mob Museum, don't know if it's open yet
Take a day trip down to the west side of the Grand Canyon and see the Skywalk
http://www.grandcanyonskywalk.com/