Responsibly Enhancing America's Landscapes Act This bill establishes the National Park Service Legacy Restoration Fund to provide funding for deferred maintenance projects in national parks. The bill increases specified fees for FY2020-FY2029 and the additional amounts collected are deposited in the fund. The fees that are increased are the entrance fees at federal recreational lands and waters, the fees for the use of the electronic system for travel authorization for certain visitors to the United States, and the fees for visa applications of nonimmigrants seeking temporary admission to the United States for business or pleasure. Amounts in the fund shall be used for the priority deferred maintenance needs of the National Park Service. At least 65% of the funds must be used for nontransportation projects.