Bring your rain boots and raincoat!
Don't bother with an umbrella....its the mark of tourist
Be sure to check out Pike Place Market. It's our local year round farmers market. I am partial to ferry rides myself, so a quick trip over to Bainbridge Island to wander around Winslow is always nice.
If you are a skier you can head up to the mountain passes just an hour or so East of the city and get in a few runs, depending on the weather.
Personally, I think the Space Needle is a waste of money. If the weather is crummy, which it most likely will be in December, you can't see much, and it's a pretty expensive ride to the top.
If you are into back to nature type things the Seattle Aquarium is nice (though not terribly cheap) You will get a true taste of PNW aquatic life. It is right on the waterfront near the ferries.
Ivar's clam chowder is a mainstay for Seattlites, if you are into coffee, the original Starbucks is located in the Pike Market area.