We've enjoyed staying at Iron Creek national forest campground off Hwy 12 near Randle. From there you can easily day trip to Windy Ridge Viewpoint of Mt. St. Helen and you can also drive to Mt. Rainier for a day hike or two. This is the 'quiet' side of both parks.
Then take 12 west to 7 north at Tacoma and 16 north toward Port Townsend. Fort Worden State Park is very nice and Port Townsend is a fun little town with lots going on in the summer. Fort Worden has nice noon concerts. For Port Townsend you can easily day trip to Hurricane Ridge for some hiking. We also took the ferry from Port Angeles to Vancouver for a day... picked up the city bus at the harbor to take us out to Burchart Gardens.
For Port Townsend you can also day trip to Seattle's waterfront. Drive down to Bainbridge Island and pick up the fast ferry which will drop you at the waterfront at the Aquarium and Pikes Market. Pick up the monorail to wisk you to the Space Needle and back to Pikes Market to pick up some delicacies and walk back to the ferry for your return.
Then I'd recommend you take 101 west and move to the Salt Creek Rec. Area for the rain forest hikes or to the Forks/Kalaloch area. Here's a great write-up on that area and camping:
https://wheelingit.us/2014/07/09/squeeze-me-and-yes-please-kalaloch-wa/Continue down 101 to Portland and return home if you're ready or else continue down 101 and the Oregon coast for awesome state parks.