Elphaba knows the city well... listen to her.
Don't forget Capitol Hill!! And the UW arboretum is lovely in the summer. How about Ballard, especially the Ballard Locks and Golden Gardens? The Nordic Heritage Museum there is a nice little gem, if you like local history.
Oh, I could go on and on. I spent 23 years there.
But I recommend you get a Lonely Planet guide for Seattle, since they tend to put out pretty high-quality stuff. Let us know how it goes!! I miss home terribly.