I have a sister in Nanning, Guanxi; also Shenzhen, Guangdong; as well as Nanjing, Jiangsu;
and Chengdu, Sichuan.

Both sentences are 'grammatically correct', and as it's ME that's writing the sentence, I can
choose which one I want to write.

Even a second semicolon in a sentence separating independent clauses is a matter of grammatical dispute.
Serial semicolons separating dependent clauses, as displayed in your example, are not grammatically correct.