National Discovery Trails Act This bill amends the National Trails System Act to include national discovery trails as part of the national trails system. Such trails (1) shall be extended, continuous, interstate trails located to provide for outstanding outdoor recreation and travel and to connect representative examples of America's trails and communities; (2) shall provide for the conservation and enjoyment of significant natural, cultural, and historic resources and be so located as to represent metropolitan, urban, rural, and back country regions of the Nation; and (3) may be designated on federal lands and, with the owner's consent, on nonfederal lands. The 6,000-mile American Discovery Trail extending from Cape Henlopen State Park in Delaware, to Point Reyes National Seashore in California, splitting into northern and southern routes near Cincinnati, Ohio, and rejoining at Denver, Colorado, is designated as a national discovery trail. The bill sets forth requirements for designation of a trail as a national discovery trail. The appropriate federal department for each national discovery trail shall (1) administer the trail in cooperation with at least one competent trailwide volunteer-based organization; and (2) submit a comprehensive plan for the trail's protection, management, development, and use.