The Hurricane Ridge Visitor Center is about 12.5 miles from the campground. From the back of the visitor center are panoramic views of the Olympic Range. There are several excellent and easy paved trails for you to explore across from the center that take you around Big Meadow. You can probably walk the paved path in about a half hour. Black-tailed deer are common and fairly tame here and an early visit may provide you with excellent deer photo opportunities.
Early summer is a good time to find mothers with their fawns.
You may also encounter colonies of marmots along the trails. This is an excellent place for summer wildflowers. Above the treeline at the north end of the loop you have views looking north over Port Angeles, the Strait of Juan de Fuca and into Canada. You will want to continue northwest another mile along the paved road to the trailhead for Hurricane Hill. This would be a great sunset or sunrise destination on a clear day.