Minerva and Arachne is one of those rare stories where the setting makes almost no difference to the story whatsoever. We know that the story takes place in the small village of Hypaepa, which was a part of the larger kingdom of Lydia. Lydia, in turn, was part of Anatolia. Anatolia is now called Turkey. So, the story takes place somewhere in Turkey. Big whoop. It could have taken place on the moon and it would have been the exact same story. Actually, it might have been better if it had taken place on the moon.

In fairness, it's possible that the story was set in Lydia to acknowledge some factual, Lydian skill at weaving. We're not sure if the Lydians were considered expert weavers, but given Ovid's tendency to set his stories in realistic locations, it's at least possible. This hypothesis is the closest we can get to a legit claim about the importance of the setting. Basically, feel free to ignore the setting unless you or one of your teachers comes up with more information.