The city council of a city of the first class shall have power to open, control, name, rename, extend, widen, narrow, vacate, grade, curb, gutter, park, and pave or otherwise to improve and control and keep in good repair and condition, in any manner it may deem proper, any street, avenue, or alley, or public park or square, or part of either, within the limits of the city or within its extraterritorial zoning jurisdiction, and it may grade partially or to the established grade, or park or otherwise improve any width or part of any such street, avenue, or alley. When the city vacates all or any portion of a street, avenue, or alley, or public park or square, or part of either, the city shall, within thirty days after the effective date of the vacation, file a certified copy of the vacating ordinance with the register of deeds for the county in which the vacated property is located to be indexed against all affected lots.