Damn that Radiant Quest! I was doing the Forbidden Quest of Gaulthur, the one were his three sons split an amulet and wreaked havok. Then a hero named Geirmund killed the sons but he died in a dual where he killed the last son. That's three dungeons to go for this quest, and the last dungeon picked was Saalthar. This dungeon is locked because, according to the wiki, it is for a College of Winterhold Quest.

It can't be completed now because my character is not a mage. If I unlock it via console, triggers and events will fail because there are supposed to be specific followers.

Bethesda, DO NOT USE Saalthar for Radiant Quests!

for me it was also Saalthar (finished it just yesterday), so I guess its not random.
Getting into a college is easy, even if you don't want to follow through the whole mage storyline. Guild's expedition to Saalthar is almost the first "real" college quest.
Did it and left the college to its own, as I'm not a mage either.

The sons are always in the same spot. He's there on purpose, not because of radiant quests. Btw, its Saarthal, not Saalthar