Grammarly Answers: Quotation Marks and Other Punctuation - Inside or Outside?

This useful article provides answers to the question by quoting the advice in several style manuals. For all but one manual, the advice is similar. Here's what my main style reference for decades--Associated Press Stylebook--says about it:

The period and the comma always go within the question marks. The dash, semicolon, the question mark and the exclamation point go within the quotation when they apply to the quoted matter only. They go outside when they apply to the whole sentence (p. 362).