I second Salty's. A little pricey, but for the view (especially if you go to the one on Alki) it can't be beat.
The waterfront is great. You can walk to Pike's Place up a bunch of stairs, or check out all the little shops right there on the water. I recommend Steamer's for the best fish & chips I've ever had.
If you're in the mood for a little drive, head east on I-90 to Snoqualmie Falls (right off the freeway). Very beautiful waterfall and a really great drive (though right now the snow is crazy, so may or may not be a great idea when you come).
I've done the underground tour, and, while cool, it's basically the same things over and over after about ten minutes. Check out Savor Seattle at
http://www.savorseattletours.com/. Lots of fun dining tours there.
Oh, and a MUST, as far as I'm concerned...Ride the Duck. It looks completely stupid but it's quite entertaining. It's basically an amphibious vehicle that will drive you around and give you a guided tour of downtown Seattle and some of the neighboring areas, and then it will drive right out and into Lake Union. Really fun and unique way to check out the city. You can get tickets at
http://www.ridetheducksofseattle.com/.
Let me know if you have other questions - I've only lived here for three years and I'm still finding stuff all over the place. Have fun!