If Durmstrang and Beauxbatons were hidden from common knowledge, how did people from other schools go to them for the Triwizard tournament?

Question

So in GoF, they state that Beauxbatons and Durmstrang are hidden from view and don't have their locations public.

“Durmstrang’s another wizarding school?” said Harry

“Yes,” said Hermione sniffily, “and it’s got a horrible reputation.

According to An Appraisal of Magical Education in Europe, it puts a lot of emphasis on the Dark Arts.”

“I think I’ve heard of it,” said Ron vaguely. “Where is it? What country?”

“Well, nobody knows, do they?” said Hermione, raising her eyebrows.

“Er — why not?” said Harry.

“There’s traditionally been a lot of rivalry between all the magic schools. Durmstrang and Beauxbatons like to conceal their whereabouts so nobody can steal their secrets,” said Hermione matter-offactly.

So how do students get to the other school for the Triwizard tournament?

Answer 1

Hogwarts was just as concealed:

“But Hogwarts is hidden,” said Hermione, in surprise. “Everyone knows that . . . well, everyone who’s read Hogwarts, A History, anyway.”

“Just you, then,” said Ron. “So go on — how d’you hide a place like Hogwarts?”

“It’s bewitched,” said Hermione. “If a Muggle looks at it, all they see is a moldering old ruin with a sign over the entrance saying danger, do not enter, unsafe.”

“So Durmstrang’ll just look like a ruin to an outsider too?”

“Maybe,” said Hermione, shrugging, “or it might have Muggle-repelling charms on it, like the World Cup stadium. And to keep foreign wizards from finding it, they’ll have made it Unplottable —”

—Harry Potter and the Goblet of Fire

Nonetheless, the delegations from the foreign schools had no trouble finding it. One presumes that Dumbledore could make the location available to the students from Beaxbatons and Durmstrang, if need be. He certainly seems to be able to remove the protective spells around Hogwarts:

As they flew over the dark, twisting lane down which they had walked earlier, Harry heard, over the whistling of the night air in his ears, Dumbledore muttering in some strange language again. He thought he understood why as he felt his broom shudder when they flew over the boundary wall into the grounds: Dumbledore was undoing the enchantments he himself had set around the castle so they could enter at speed.

—Harry Potter and the Half-Blood Prince

A similar situation probably holds with Durmstrang and Beauxbatons: they can simply alter or remove their spells to allow in foreign students. In particular, given that the delegations only arrive on a single day, they would only need to lift their protective enchantments for a very short period.

Answer 2

Durmstrang’s visitors agree to be charmed to forget the way to it.

Hosting people from other schools wouldn’t be a problem for keeping where Durmstrang is a secret. Visitors to Durmstrang have to agree to have memory charms used on them so they forget how they got there and its location remains secret. Visitors coming for the Triwizard Tournament would presumably also be required to agree to have memory charms used on them.

Although believed to be situated in the far north of Europe, Durmstrang is one of the most secretive of all schools about its whereabouts, so nobody can be quite certain. Visitors, who must comply with memory charms to erase their knowledge of how they got there, speak of vast, sprawling grounds with many stunning views, not least of the great, dark, spectral ship that is moored on a mountain lake behind the school, from which students dive in summertime.
_{^{- Durmstrang Institute (Pottermore)}}

It’s not mentioned how Beauxbatons controls what knowledge Triwizard Tournament visitors leave with, but this at least gives an idea what one of the participating schools handles this.

Answer 3

There are, according to Hermione, two layers of charms applied to the schools; Muggle-repelling charms and unplottability. The Muggle-repelling charms make the schools invisible to muggles, but not witches and wizards. The unplottability makes the school invisible to witches and wizards and prevents the school from showing up on maps.

Since students (and teachers) regularly leave Hogwarts and come back again, there must be some sort of loophole that allows those with the permission of the school's management to come and go without falling foul of the unplottability. It can be assumed that the Ministry of Magic would coordinate permission being given to delegates of foreign schools to see through the illusions and to come to the schools in the event of an international tournament.

Their locations may be a general sort of secret, but it beggars belief that after a thousand years, everyone in the wizarding world who needs to know where these schools are, doesn't actually know exactly where they are.