Ha, my brother and I were just complaining the other day how little we know about geology and our good friend who has an undergrad in the field, has said he's just barely scratched the surface on the topic (no pun intended). We were comparing what rocks and formations we've come across throughout the state (I've found slate, he hasn't....side note, my friends find it odd that on hikes I'll stop to bang rocks together).
Airbnb is the place to look for accommodations, it's people renting out extra space to travelers, has a wide variety of sleeping arrangements, from people renting out a spare room to mother in law apartments and even whole apartments and houses.
Second the idea of taking a ferry out to Bainbridge, seeing the Olympics to the west and the Cascades to the east, guarantees great photo ops.
Also second the suggestion of renting a kayak, see the floating homes, and it's awesome if you can time it for rush hour, it's fun to kayak faster then the cars moving on the bridge, as you kayak underneath them, just mind the paddle, with the low clearance.
A little on the spendy side, but still fun is the walking Underground Tour of Seattle, learn about the time the city had exploding toilets and about the purple glass in some of the sidewalks.
Pikes Place for the flying fish and seeing cheese getting made, google happy hour specials to get deals on drinks and food, and finally there is a 3 story restaurant in the market that has amazing views, but again on the pricey side.
As for the rest of the state, family favorite road trip is taking the Northern Loop highway aka highway 20, I'm sure you already plans, but if you can squeeze in this road trip it would be well worth it, breathtaking scenery and great hikes.
Eastern Washington is wine country, but Woodinville, about 30 mins northwest of Seattle, is where a lot of those wineries have tasting rooms, also the Red Hook Brewery has tours with lots of sampling encouraged :)
Final piece of advice hit up the local Rangers station, they're the perfect matchmaker between hiker and trail. You let them know what you're looking for, elevation gain, views, lakes, difficulty, time and they'll find you the perfect hike and get you directions to the trail head.
Hope you have a great time!