Hmm I can't help overall because I've never traveled around there, but I do have family in Seattle and my best advice in that regard would be "don't stay long". Seattle has some cool sights worth maybe checking out but overall my impression of it is that it's a pretty depressing city to hang out in.
It's only depressing if you come here in the middle of the winter when the weather is horrible. It's much better to be here if you come in the summer, like he is, when it's actually sunny most of the time.
There's not much here that others haven't already suggested, but I'll add in Mt. Baker and St. Helens if you haven't already seen enough mountains. While you're in the city itself, the Space Needle is worth considering if you like the view, although the food is ridiculously expensive. There's some other things in the city worth visiting, but most of the things you'd want to see around here are the aforementioned national parks, rivers, and mountains.