Our son & family have lived in the Seattle area for over 20 years so we're now pretty well acquainted with what is here. Other than what has already been mentioned, here are some suggestions for your consideration:
1. Chihuily blown glass museum downtown (
http://www.chihulygardenandglass.com/)
2. Seattle Acquarium along the downtown waterfront (
www.seattleaquarium.org/)
3. Ray's Boathouse restaurant in Ballard, about 5 miles NW of downtown (
http://www.rays.com/)
4. And while you're in Ballard, stopping by to see the
Hiram M. Chittenden Locks (
http://www.nws.usace.army.mil/), where boats go from Lake Washington and Lake Union into the Puget Sound is pretty cool to see.
5. Seattle Museum of Flight (
http://www.museumofflight.org/) just south of downtown
6. Water tour of Lake Washington (I think you can see Kenny G's and Bill Gates' houses on such a tour)
7. Lake Union & Chandler's Crabhouse on the north edge of downtown (
http://www.schwartzbros.com/chandlers-crabhouse/) where you can watch the float planes land and take off.
8. Mt. Ranier National Park (
http://www.nps.gov/mora/index.htm)
9. Mt. St. Helen's (
http://www.fs.usda.gov/mountsthelens) it is amazing to see how much got blown away
10. Poulsbo, WA---a really neat Scandanavian community about 1 hour NW of Seattle {
http://www.mapquest.com/#c7cb785bd0112e6a26caf391} (
http://www.tripadvisor.com/Tourism-g58688-Poulsbo_Washington-Vacations.html)
You probably won't get it all in, but this should give you lots of good choices which will help you absorb the culture in Seattle!!