Paria Canyon, Arizona. Camping in a side canyon of the Paria River in the Paria Canyon -Vermilion Cliffs Wilderness Area in northern Arizona. The normally-small stream known as the Paria River has carved one of the most beautiful canyons on the Colorado Plateau. The river's headwaters begin in the Pink Cliffs of Bryce Canyon National Park 60 miles northwest of this location. The river eventually drains into the Colorado River 15 miles downstream at Lee's Ferry at the entrance to the Grand Canyon. Along the way, soaring vertical walls of Navajo Sandstone line the river, reminiscent of the cliffs of Zion National Park.