I used to be a local, so I haven't done many of the "tourist" things to do. A few things I would suggest for a tourist though:
The Mariner's are at home against the Angels during your trip.
Unless you really want top seats just purchase the cheapest ticket possible (bleachers) and then watch the game while checking out the stadium. I normally spend my time in the beer garden (center field).
http://seattle.mariners.mlb.com/
There is also a Pyramid alehouse across the street from the stadium, so if you're going to be going to a weekend game it should be packed before the game. They typically close off their parking lot and have it set up more like beer tents.
http://www.pyramidbrew.com/
There are a lot of good wineries and breweries in the area. I would recommended checking out Woodinville if you are into that. There is the Redhook brewery, and 2 wineries right across the street from one another.
The redhook tour is only $1 and you get to taste all their beers that they are brewing at the time & a souvenir glass.
I can't remember how much the st. Michelle tour is.
The other winery, I can't remember the name of, they don't offer tours, but for something like $5 you can go in and get a taste of 5 or so different wines that they have.
www.redhook.com
http://www.ste-michelle.com/
A few more things:
http://en.wikipedia.org/wiki/Gum_Wall
http://en.wikipedia.org/wiki/Fremont_Troll
Depending on how far you would like to travel while there, a lot of tourists make a day trip out to Leavenworth.
http://en.wikipedia.org/wiki/Leavenworth,_Washington