Learn English – Is it ever acceptable for a period to come after a quote at the end of a sentence?

The British put them outside the quotes, which seems much more logical.

The American style is to put the punctuation inside the quotes. The American version is often known as "Typesetter's Quotes".

As you can see, I go with the British version, at least in informal writing.

Interesting fact: They are called typesetter's quotes because when typesetters were laying out the typesetting blocks putting the small blocks for punctuation inside the quotes made the layout more stable and less prone to shift around. That's probably why it seems so illogical, it was done for mechanical reasons, not linguistic reasons.