San Gabriel Mountains Foothills and Rivers Protection Act This bill establishes the San Gabriel National Recreation Area in California as a unit of the National Park System, consisting of approximately 51,107 acres of identified federal lands and interests. The Department of the Interior must cooperate with the Department of Defense (DOD) to develop opportunities for the management of the federal lands under DOD jurisdiction that are included within the recreation area. The bill establishes the San Gabriel National Recreation Area Public Advisory Council and the San Gabriel National Recreation Area Partnership. Interior and the San Gabriel National Recreation Area Public Advisory Council shall create a comprehensive management plan for the recreation area. Interior shall develop an integrated visitor services plan for the recreation area and is authorized to construct visitor use facilities. The Department of Agriculture must modify the boundaries of the San Gabriel Mountains National Monument in California to include approximately 109,143 acres of additional, identified National Forest System lands and administer them as part of the monument.