Is a comma placed inside or outside of close quotes at the end of a sentence?

The question should be:

Is a period placed inside or outside of close quotes at the end of a sentence?

It depends on the style guide you're using, and whether your publication is to be official in the 'American English' or 'British English'.

In American English, you'll place the period inside the close quotes. In British English, you'll place the period outside the close quotes.