As a grammar queen (king?) myself...
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The placement of question marks with quotes follows logic. If a question is in quotation marks, the question mark should be placed inside the quotation marks.
Examples: She asked, "Will you still be my friend?"
Do you agree with the saying, "All's fair in love and war"?
Here the question is outside the quote.
NOTE: Only one ending punctuation mark is used with quotation marks. Also, the stronger punctuation mark wins. Therefore, no period after war is used.
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In college, I was told that punctuation ALWAYS goes in quotation marks, but that's wrong; it should follow logic. As my own example (I copy and pasted the above from a reliable website):
Did you like "To Kill A Mockingbird"?
looks much better than...
Did you like "To Kill A Mockingbird?"
Putting the punctuation within the quotes there looks like the title includes a question mark.
Conversely, if you're quoting a phrase, the appropriate punctuation should follow within the quotation marks.
Oscar Wilde once declared, "Either the wallpaper goes, or I do."
That is correct. This...
Oscar Wilde once declared, "Either the wallpaper goes or I do".
...is not.