The Council shall have power to close and/or vacate any street or alley, or any part thereof; provided that it shall not have power to vacate or alter any State or County highway. When the Council shall deem it advisable to vacate any street or alley or any part thereof, it shall, by resolution, so declare and in the same resolution shall appoint a time, not less than four weeks thereafter, when it shall meet and hear objections thereto. Notice of such meeting, with a copy of said resolution, shall be published two successive weeks before the appointed time for such meeting, in the official newspaper of the City, and posted in not less than three public places on the street, alley or part thereof proposed to be vacated or abolished.