La Plata River is a 70-mile-long tributary to the San Juan River in La Plata County, Colorado, and San Juan County, New Mexico, in the United States. This small river heads at the western foot of Snow Storm Peak in the La Plata Mountains of southwestern Colorado, approximately 35 miles north of the New Mexico state line. It flows in a southerly direction unt…La Plata River is a 70-mile-long tributary to the San Juan River in La Plata County, Colorado, and San Juan County, New Mexico, in the United States. This small river heads at the western foot of Snow Storm Peak in the La Plata Mountains of southwestern Colorado, approximately 35 miles north of the New Mexico state line. It flows in a southerly direction until it joins the San Juan at the western edge of the city of Farmington, New Mexico, about 19 miles south of the Colorado state line.