For multi-day wilderness adventures, Rangers told me the higher, dryer east half Olympic National Park was best. Many options depending on how many days you have.
Just looking at a map, I’m thinking to start at Deer Park trailhead (5400ft) because it’s high. Decide where to exit based on Ranger’s advice, weather and the number of days I’ll have.
Leave a comment if you’ve hiked overnight on the East side of the Park.
besthike.com 
Be sure to bring the newly released Olympic Natioanal Park app by Chimani (http://www.chimani.com)