Northeast of Aberdeen and Lake Quinault, the East Fork Quinault River Trail is by far the most popular backpacking route in the park since it passes through the Enchanted Valley. From the Graves Creek trailhead, its a 13+ mile hike up 1400 feet to the beginning of the Enchanted Valley, a vast glacial cirque with numerous waterfalls tumbling off the sheer cliffs. Think of it as a mini Yosemite in a temperate rain forest of hemlock, cedar and bigleaf maple.
An alternative route is to hike over Andersson Pass from NFS Dosewallips CG -- the overall distance to the Enchanted Valley is half but theres 2400 of vertical each way.
To reach the primary trailhead from Aberdeen, follow US101 north to Lake Quinalt. Head northeast on South Shore Road for 19.2 miles to Graves Creek trailhead. While on Graves Creek Road, watch out for large bull Roosevelt Elks!
Overall, East Fork Quinault River Trail (Enchanted Valley) is the 6th most popular hiking trail of all 56 hikes in Washington.