Someone (a girl) who wears out-of-control clothing that isn't even fashionable. Also, they strut like they are on a mission--however, they do not know where to go. They also think they are an asset to society, when in fact, they are regarded as ridiculous.
The term is used as a joking description of the person seeing as if they were really thrown out to be independent in a city they would be lost, laughed at, and confused.
An example of an independent city girl is a girl wearing lace up heeled boots and a lace dress with a trench coat while strutting the halls looking for fashion ideas. This girl on a mission would be described as an independent city girl.