I second the underground tour. Very wry, very funny (at least the woman who led us through was). And I went as a resident...
As a nature freak, I'd hit the Olympic Peninsula and Vancouver Island (and the coast of Oregon, for that matter). It depends on what time of year you're here, of course, and how long you've get (by ferry or by road, both are a pretty decent trek).
Honestly, as far as I'm concerned, there's nothing much you can do in Seattle that you can't do in Beantown. Can't vouch for Portland. I love going to 13 Coins to eat when I've got a few extra bucks; not a very good option for the cash-strapped or the vegetarian. The clams (appetizer menu, lots of garlic) are unbelievable.
The fabulous local (and only local, so far as I can tell) beer: Mack and Jack's African amber. Mmmm, like a big, fat, chewy IPA, dry-hopped to high heaven with our own Cascade hops. Mmmmmmmmmmmmmm..........
Would make more and better suggestions, but I'm generally pretty strapped for ideas myself. Pretty much any boat trip in the Puget Sound is a winner.
Oh! Three pieces of Seattle public art that I think you'd dig, all in the Fremont neighborhood:
The Fremont Troll
Waiting for the Interurban
All very close to my house, and some of the most original things Seattle's got outside of the Pike Place Public Market (also worth a look, though much more antiseptic than it used to be).