Let it be said: this is not an official review. My husband and I thought we would head out to backpack the Redwoods, but found out you have the be a pretty serious through hiker in order to take full advantage of the backpacking sites. Most are a short hike off the road, making them almost car camping sites. Many of them are free with a permit from the park. However, we learned that folks camp up there without permits and all the sites can theoretically fill up, so make sure to claim yours early.
Generally speaking, your best bet will be to call the visitor's centers for information. I scoured the web in an attempt to find a good plan or recommended hikes, but came up short. Once we stopped at a visitor's center, the parks staff was incredibly helpful and friendly. The are the Hiouchi Information Center, the Jedediah Smith Visitor Center, the Crescent City Information Center, the Prarie Creek Visitor Center, and the Thomas H. Kuchel Visitor Center. Call at least a couple as they'll have different information specific to their location. In fact, one visitor center was able to ward us off from a particular backpacking camp site because there had been a recent rash of break-ins.
Rangers, rangers, rangers! I can't say it enough. They are your key to an excellent trip to the Redwoods. We wound up spending a couple of days driving through the Redwoods and doing short day hikes, adding a day starting and ending around the park for the Tall Trees Grove. If you can swing it, this is definitely worth it! Due to foot issues, we never got to see the Dolason Prarie Trail that shoots off from the Tall Trees access point, but it sounded excellent. However, if you're backpacking that area - don't be fooled. The "gravel bars" tend to be rock bars and you'll definitely want some good footware for wading as there will be plenty of it.