The southern end of Olympic National Park’s [1] coastal strip is the most accessible, with Highway 101 running right along the bluff for more than a dozen miles. Short trails lead down to the water at half a dozen points, and at the southern end one finds the town (of sorts) called Kalaloch [2], with a comfortable lodge, two Park Service campgrounds, and other facilities.
Beach camping is not allowed along this stretch of the coast.
Links:
[1] http://www.moon.com/destinations/washington/olympic-peninsula-and-the-coast/olympic-national-park
[2] http://www.moon.com/destinations/washington/olympic-peninsula-and-the-coast/olympic-coast-and-hoh-rain-forest/ruby/kalaloch