Several trails head up the Sol Duc Valley [1]. A favorite is the one-mile Sol Duc River Trail, which passes through enormous western hemlocks and Douglas firs to Sol Duc Falls, one of the state’s best-known waterfalls. A footbridge crosses the deep gorge cut by the river.
From here, you can climb another three miles (one-way) to Deer Lake, bordered by trees. For variety, return to the campground from Sol Duc Falls on the Lovers Lane Trail, a three-mile path along the south side of the river.
A fine loop trip for backpackers (wilderness permit required) is to head up the Sol Duc River Trail to Seven Lakes Basin, then uphill to the summit of Bogachiel Peak and back out for a round-trip of 22 miles.
Links:
[1] http://www.moon.com/destinations/washington/olympic-peninsula-and-the-coast/port-angeles-sol-duc/sol-duc