The Philosopher's/Sorcerer's Stone was guarded first in Gringotts (which had never been robbed until the events of the book) and then later was moved to Hogwarts (where it was pretty well protected). After Harry stopped Voldemort from getting it, Dumbledore says that he and Nicolas Flamel decided that it was best to destroy the Stone to prevent it from falling into the wrong hands.
But why not hide it in a place protected by a Fidelius Charm*, either after removing it from Gringots or after nearly losing it at Hogwarts? It seems like you could just have Nicolas Flamel as the secret-keeper (who might reveal it to Dumbledore), and then nobody, including Voldemort, could ever find it.
I realize that out-of-universe, this is because Rowling hadn't invented the concept yet, and in the case of bringing it out of Gringotts, it would have been Harry Potter and the Boring First Year if it were immediately hidden by the Fidelius Charm instead of being taken to Hogwarts. But I'm wondering if there was an in-universe reason why it might have not been hidden using the charm.
I suppose that maybe it was moved from Gringotts to Hogwarts to draw out Voldemort on Dumbledore's turf, but I'm not sure why they wouldn't hide it afterwards.
So why not hide the Philosopher's/Sorcerer's Stone with a Fidelius Charm?
* For more info on a Fidelius Charm and it's rules, check out Precisely How Does the Fidelius Charm Work?