I personally know that there are two public offices. One is located in Laoshan District, Room 404-407, the fourth floor of Kaixuan Commercial Center at the southernmost tip of Haier Road. The other is in sifang district, in a big garden with the People's Road sifang district Procuratorate. You can find a public office by asking the Sifang Procuratorate.
Each of the four districts in Qingdao has a public office, and I don't know the rest. Good luck.