Commas and Periods Always Go Inside…
Commas and periods ALWAYS, ALWAYS, ALWAYS go inside the closing quotation mark in standard American English. Period.
1) I really like the word “cheese.”
2) He said, “I really like cheddar cheese.”
3) “I do like cheese,” said the mouse, “when it’s not baiting a trap.”
In every case, and these examples are not exhaustive, the comma and/or period is ALWAYS inside the closing quotation mark.