There’s nothing at all unBuddhist about this quote, or the sentiment it expresses, but as far as I’m aware “Peace comes from within. Do not seek it without.” isn’t found in the Buddhist scriptures.
It sounds like someone has tried to distill the Buddha’s teaching into a nice maxim, and hit on a saying that was already popular.
This probable Fake Buddha Quote seems to have been around for some time. According to Google Books, it’s found attributed to the Buddha in Distilled Wisdom: An Encyclopedia of Wisdom in Condensed Form, by Alfred Armand Montapert, from 1964, although it has to be said that Google Books’ dating is sometimes off. And Google also says it’s found in a 1959 book by George Francis Allen, with the splendid title of Words of Wisdom: The Buddhist Companion Book; Containing 365 Maxims and Utterances Attributed to Gotama Buddha for Each Day and Night of the Year.
Something very similar is found in an 1873 book, A Twofold Life, by Wilhelmine von Hillern:
“There is also a heaven upon earth in our own breasts. Do not seek it without, but within your heart ; then you will not come into heaven for the first time when you die, but remain in it always.”
The saying was around in 1907 as “For the spirit of contentment and peace comes from within, not from without.” (Library Journal, December, 1907), and in 1908’s Country Life magazine as “Peace comes from within, not from without,” where it is described as “the message of Marcus Aurelius.”
I haven’t found any instances before the 20th century, but in “The Complete Words of W. E. Channing,” I’ve found the following:
“There can be no peace without, but through peace within. Society must be an expression of the souls of its members.”
This is from a lecture, “On War,” delivered in 1838. The general idea is no doubt much older, but the expression “peace comes from within” seems not to be much more than a century old.