Be sure to visit Mt Rainier National Park which is a must-see attraction. There's also Olympic National Park but its located too far away from Seattle and only doable with a night nearby. Suggest u only visit Rainier unless you like hiking in parks.
Seattle's home to Boeing so there's quite a few avionics attraction in town. Museum of Flight is located 10-15mins south of downtown and is home to, among other views, the only Boeing 747 prototype and a Concorde. Worth a visit especially if you purchase the
CityPass which provide passes to several attractions at a discounted rate. Another one is Boeing's Future of Flight museum, not to be confused with the other museum above, which also have a tour available to Boeing Everett factory where you can actually see assembly of current planes(producing 747s and 787s now). No photography is allowed during the tour though. Also its located 50 miles north in another city Everett so you probably have to get a day tour to avoid getting expensive taxi fares.
Downtown Seattle contain the rest of the attractions i.e Space Needle, Starbucks #1 store etc.
Be sure to visit
Kerry Park in Queen Anne. It's a tiny park in a residential area but provide an award winning view of Downtown Seattle. I'll probably skip University District if i were you though, the area's unsafe with significant crime rates.
From Seattle, you can do day trips to Victoria,BC or Vancouver, BC. Amtrak trains run north to Vancouver B.C at 7am arriving at 11am. The last train depart for Seattle at 5-6pm which give u 6 hours or so to explore downtown Vancouver. Victoria,BC is doable via a ferry ride across.
For a reference, here's a sample itinerary:
Day 1: Downtown Seattle/Space Needle/Museum of Flight
Day 2: International District/Capitol Hill/Fremont/Kerry Park in Queen Anne/etc
Day 3: Mt Rainer day tour
Day 4: Boeing™ Assembly Plant & Future of Flight Aviation Center tour (half day) / Bellevue
Day 5: Day tour to Victoria, BC / Butchart Gardens via Victoria Clipper / Vancouver,BC
I've done quite a lot of research for Seattle because the above itinerary was my original plans for a future trip. If any of the above info is inaccurate, do accept my apologies.