National and Regional Greenways Act This bill requires the Department of Transportation (DOT) to establish a grant program for states, localities, and tribes to support community greenway paths for walking, bicycling, and other motor vehicle alternatives. DOT must designate eligible greenway paths that are considered regionally or nationally significant through a national greenway paths network; paths must cross multiple localities or states, reduce congestion, improve safety, benefit the environment, support communities, or meet other specified criteria. Eligible projects must support access to public parks, transportation, and other community needs.