I do think a car is the way to go @cavaaller as it'll give you the most options. And our roads will feel sufficiently familiar to you. One day you could head to Mt. Rainier NP. The next day you could head out to Olympic NP. Personally, I'd want one day in the mountains, a second day on the seashore and possibly a 3rd day at one of Seattle's great museums followed by some urban time in Queen Anne, Fremont or Ballard. Seattle is a stunningly beautiful place to visit with loads of outdoor recreation at your fingertips. The locals can do a great job guiding you.
Oh, they also brew some darn good beer! 🍺