It didn't cost us anything, we did not stay overnight...
I don't believe it costs to go into the park. We visited the Avenue of the Giants at no cost! There are a few attractions through it that cost about $10. As far as camping goes I don't know, we didnt stay
I believe the "State Rate " at any state owned campground is $35 per night. They have limited TV or trailer spaces and some of the campgrounds requires reservations of up to 6 months or more. Cancellations do happen so call ahead. Humboldt Redwoods has several options for camping. Go to the web site and check it out.
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