A few years ago, they became such pests that park rangers tried driving them off with paintball guns. Years ago, mountain goats were almost as common as deer, but a decade long purge of goats in the park has made them a rare sight, indeed. You've a better chance of seeing a berry-gobbling black bear in the meadows below the paved Hurricane Hill Nature Trail or in the high country around Waterhole on the Obstruction Point Road. Take the Whiskey Bend Road just past the Elwha Ranger Station for car-window peeps of blacktail deer and perhaps elk, and walk the Elwha River Trail about 0.5 miles to the Elwha overlook for views of elk along the river below. You might also spot elk in the rain forest along the river just across the Elwha bridge at Altaire.
Elk also wander through the campground from time to time.
Look for elk along the highway anywhere from Greenwater to the south. Best viewing chances in the park might be around the White River Entrance, along the first mile of the trail to Summerland, or along the White River Road. Look along the high, rocky ridges that run north from the big hairpin parking area just east of Sunrise or in the rock ridges of Burroughs Mountain, southwest of Sunrise. You may also see black bear in the high meadows. Look in the fields along the south side of the road, early in the morning.