You're into Hiking — get out onto a day hike at Mt Rainier. Lots of trails you can do in a couple of hours. Washington state is about being outdoors. http://www.everytrail.com/best/hiking-seattle-washington
And you like fresh simple food — get to Pike Place Market and pick up fresh wild salmon, local oysters, whatever. Fantastic fresh food.
Rent a bike and check out Georgetown, a short ride out along the waterfront to an old industrial area that's got a great hip vibe for coffee, beer, hanging out. Capitol Hill, up to the lake — the hills will be a challenge if you're not used to them on a bike.
Stand out tourist places of course are: the Space Needle, the EMP (http://www.empmuseum.org/), and taking the momorail from downtown out to the old world fair grounds. People like the http://www.chihulygardenandglass.com/ — it's right at the Needle. The Seattle Art Museum SAM has a downtown location. There's a walkable sculpture garden along the ocean downtown. Washington state was a leader in legislating 1% of construction budgets going toward art, so there's a big public art presence there. And the area around Occidental is a good feel of 19th century Seattle.
next trip out schedule another day and take the catamaran from Seattle to Victoria and I'll show you around.