In the downtown area, you can visit the Pike Place Market (home of the flying fish), the Seattle Art Museum, the Space Needle is fairly close to downtown, and the waterfront pier area (with the Ye Olde Curiousity Shop). There's also some good shopping downtown too, with major stores like the flagship Nordstrom store, Macy's, and an assortment of boutiques and high end fashion shops.
The duck tour is also supposed to be pretty good:
http://www.ridetheducksofseattle.com
Have fun!