Go on the Duck tour (duck boats), the Underground City tour, Pike Place market is always fun. If you stay downtown, you can actually get away without renting a car. We stayed for a week and either walked or took the bus. If you stay with a certain zone, the bus is actually free during certain times. We also checked out the International village and the museums.
You can take the Victoria Clipper up to Victoria, BC (about 2 hours one way) and go see Buchart Gardens in Victoria. Definitely, go to Tillicum Island and enjoy the Salmon Bake and show. That's a lot of fun. See what is offered on the Seattle CityPass (
http://www.citypass.com/seattle). If you want to go to all those places offered, it is a great deal.
The museum that gmcsewer is talking about is the Boeing Air Museum at Boeing Field. It is a great museum.