The Quillayute River is a river situated on the Olympic Peninsula in Washington. It empties to the Pacific Ocean at La Push, Washington. The Quillayute River is formed by the confluence of the Bogachiel River, Calawah River and the Sol Duc River near the town of Forks, WA. The Dickey River joins the Quillayute from the north, just above the river'…The Quillayute River is a river situated on the Olympic Peninsula in Washington. It empties to the Pacific Ocean at La Push, Washington. The Quillayute River is formed by the confluence of the Bogachiel River, Calawah River and the Sol Duc River near the town of Forks, WA. The Dickey River joins the Quillayute from the north, just above the river's mouth at the Pacific Ocean.