San Juan river, Utah. The San Juan River in southeast Utah provides 85 miles of mostly-calm water from the Sand Island put-in near Bluff to the take-out at Clay Hills Crossing. The river is occasionally interrupted by class II or III rapids. Downstream of the town of Mexican Hat, the river enters the Goosenecks of the San Juan and takes on the look of a scaled-down version of the Grand Canyon as red limestone cliffs rise high above the water.