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 51,107 acres of federal lands and interests in land. The Department of the Interior must (1) 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, (2) create a comprehensive management plan for the recreation area, and (3) develop an integrated visitor services plan for the recreation area. The bill establishes (1) the San Gabriel National Recreation Area Public Advisory Council to advise Interior on the development and implementation of the management plan and the visitor services plan, and (2) the San Gabriel National Recreation Area Partnership to coordinate activities of governmental and private entities in advancing the purposes of this bill and to improve management and recreational opportunities within the recreation area. The Department of Agriculture must modify the boundaries of the San Gabriel Mountains National Monument in California to include 109,143 acres of additional, identified National Forest System lands and administer those lands as part of the monument. The bill designates (1) specified areas as components of the National Wilderness Preservation System, and (2) specified river and creek segments as components of the National Wild and Scenic Rivers System.