Rockefeller Forest
It's a lesser used part of the Humboldt Redwoods State Park.
This might take you there, otherwise just google:
Has a very large, less used/less developed campground.
Mid-week/Mid May is no guarantee of campsites along the Ave.
Humboldt Redwoods State Park
Humboldt Redwoods State Park is a state park of California, United States, containing Rockefeller Forest, the world's largest remaining contiguous old-growth forest of coast redwoods.
Wikipedia
Area: 80.7 sq miles (209 km˛)