Does the comma go inside the quotes? "Ex. "I don't want to eat that," said Mark.
No. See explanation.
The correct form is (in my opinion) "I don't want to eat that.", said Mark.
If the comma is inside quotation marks it would mean that some words are missing from the quote and it would probably be written using "..." like:
"I don't want to eat that, (...)", said Mark
Convention states that punctuation marks that are part of a sentence, even if they are not part of the original quotation, belong inside the quotation marks.
So, there is a comma in the sentence
"I don't want to eat that," said Mark.
Similarly, one would also write
Mark said, "I don't want to eat that."
with the period contained within the quotation marks.