I'll throw in a suggestion of the flightseeing tour with Kenmore Air. They operate out of south Lake Union (not far from the Space Needle). The two hour tour out to the San Juan Islands and back is awesome!
Well worth it and can easily be fitted into and afternoon or morning.
If you want to fill a full day, then a drive around the Cascades Loop is ideal. The route home takes you through Leavenworth, and you'll cross a couple of passes heading over and back to/from the Eastern side of the state. It's amazing to see the desert in Eastern WA. Figure between 12 - 15 hours for this road trip with fuel, photo breaks and dinner. Stick to the speed limit, too. Areas can be well enforced.
if shopping is your thing, as mentioned hit Pike Place, but University Village in Seattle is a great place, as arethe outlet shops in Tulalip (call this 45 minutes or so from Seattle).
I'll include a shout out for dinner at an excellent little spot I recently learned of. Cafe Veloce in Kirkland. Great Italian food, food prices all stuffed inside a space covered in motorcycling memoribilia (sp?), with real Italian brand racing bikes on the walls. The actual bikes themselves. We had dinner with a '50's era Ducati 250cc road racer last night, in fact.
Rain here falls straight down for the most part. Before younscoff, this generally indicates a lack of wind, so an umbrella works just fine. Pack a light jacket (waterproof) and you're good to go. Don't let a day of forecasted rain dampen you mood. Many days rain on and off, so just get out and enjoy. The city offers lots to explore and lots of thoughtful spots to stop under awnings to stay dry.
one warning about snow. Snow isn't the issue here. The issue is people don't know how to drive properly in it, so it gets a bit "Mad Max: Beyond Thunderdome" when it snows. I moved here recently from Eastern Canada and have been here each month over the two years previous - this isn't real snow. For real snow, head to the highlands/mountains.
. Just be mindful of IF we do get snow, the highways get interesting as people panic. Nothing for YOU to panic about, though, as this mild state of flurry-based hysteria usually just adds some time to the commuting. If a few inches go gather on the ground, though, the city gives up, shuts down and brings in a Shaman to dance for more rain.