There are many things to see in Seattle. I have lived there for a year and I would definitely go up to the Space Needle. There is a restaurant on top that turns continuously so that you have a wonderful view over the whole city. Moreover, I can recommend the Underground tour and the Pike Place Market. And if you love coffee there is the first Starbucks very close to Pike Place Market. You should also go to one of the many lakes that surround Seattle like for example Green Lake or Lake Union (where parts of "40 things I hate about you" were shot). Other things to see are the Bill Gate's House, the Boeing Factory and the Fremont Troll.
I hope you will enjoy your stay!