No time for Olympic? That's a shame, as there are some great places to do short hikes in that park. I think we did four or five on our trip. I was going to suggest some of them.
In Seattle, your teen might enjoy the Space Needle (you will, too), Pike Place Market, or the Museum of Pop Culture. If you've the time, try one of the ferries out to the islands -- friends of mine rave about using them to go see their son on Bainbridge Island.
In Redwoods NP & SP's, there are lots of short hikes in old-growth forest, check out this link!
Donna