On the way down, maybe something like this.
1 N - Cape Disapointement Sate Park, easy walk from camp through the dunes to the beach/ocean. Visit the Lewis & Clark Interpretive Center. Drive to the end of Jetty Rd. and watch the Pacific Ocean and Columbia River meet/collide, amazing sight.
2 N - Florence area via Astoria and the coast. The Oregon Dunes are pretty cool, run the kids ragged in the sand. Maybe camp in Jessie M. Honeyman Memorial State Park. Bit of a long drive but very scenic, lots to do in the area.
1 N - Jedediah Smith Redwoods State Park, nice park. Easy flat walk from camp over the walk bridge over the Smith River into Stout Grove, it's a fairy tale Redwood Grove, really beautiful and easy hike.
2 N - Humboldt Redwood State Park. another outstanding area, very cool Redwoods. I like the camping best west of Hwy.101. You might enjoy Albee Creek Campground, more away from the people, the drive to it is amazing, Avenue of the Giants is awesome.
On your way south of Crescent City/Jedediah you might like " Trees of Mystery ", it looks pretty tacky from all the tourist signs along the way but the Indian museum gets great reviews here.
Also keep an eye out for the Elk Herd around Orick, ask around. Kids will love it.
IMO, Redwoods National Park is pretty overrated and will be a big disappointment after Jedediah and Humboldt, will save you a little driving.
Drive to SF via Hwy.101.
On the way up.
1 N - Lassen Volcanic NP, very underrated place, camp in the park. If it's crowded Hat Creek Campground just north of the park is fantastic.
1 N - Crater Lake. Camp at Jackson F. Kimball State Recreation Site just before the NP, it's OK, good place for the night. No camping in Crater NP.
2 N - Sisters. Next morning after Kimball do a drive around Crater Lake, east side. It's a very beautiful place but not much to do.
Then drive up to Sisters via Bend, maybe have lunch and drive Hwy.20 to Suttle Lake, maybe Blue Bay Campground, several campgrounds on the south side of the lake. The Willamette National Forest area is incredibly scenic, great driving, any campgrounds and few people.
The drive from Suttle back to Seattle is a little long but not bad and the scenery of Willamette NF, makes up for it.
I'm guessing you have been to Columbia Gorge but if you haven't maybe camp the last night at a state park just east of Portland, it's a very scenic-jaw dropping area and make the drive back to Seattle easier.