The street superintendent shall also cause a notice similar in substance to be published for six days in a daily newspaper published and circulated in the city, and designated by the city council for that purpose, or in cities in which there is no daily newspaper, he shall cause the notice to be published by two insertions in a weekly newspaper so published, circulated and designated. If there is no daily or weekly newspaper published in the city, the notice shall be posted for six days on or near the council chamber door, and in two other public places in the city.