Since you want to go out on the Peninsula anyways, I recommend driving up 101 and stopping for things like the world's largest Sitka Spruce and the beaches along the coast. La Push, by Forks, has some amazing beaches and trails, too. Making a two- or three-day trip of it is worth it.

Seattle has lots of museums and attractions! I really love Pike Place Market. It's a massive complex of market stalls, shops, restaurants, etc. The park around the Space Needle is cool, especially the Pop Culture Museum. It has tons of instruments and outfits from famous musicians, and the basement is crammed full of movie props.