My last boyfriend said I was “simply the best.”

The exception I refer to above would be if you there were 2 puncutation marks needed depending on the nature of the quotation. For example, you could have said:

My last boyfriend said I was “simply the best!”.

Then, since what your boyfriend said was an exclamation, the exclamation point would be within the quotation marks, but since you are simply stating it, the period of YOUR statement is outside. As I said, this is an extremely rare exception to the “always inside the quotation marks” rule.

Mary said “I’m going to the store”, and then she left.

“I’m going to the store.” Said Mary, and she left.

In your example, the quote is part of the sentence, so it would be:

My last boyfriend said I was “simply the best”.

The period (or any punctuation for that matter) always goes inside the quotation marks.

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Period inside the quotations.