The Rito party winds down eventually. Link calls them from the little device they gave her once, just to make sure it worked.

They eventually get enough information about landmarks to tell how to get to their intended destination of Hateno Town - Go southeast carefully, (avoiding the dark castle) until you see the Dueling Peaks, a mountain cleanly split asunder (by dragons, the legend says), head straight through those and keep going until you see a big town built on a long upward slope with the lighthouse-like Ancient Tech Lab at the very top.

Nothing particularly catches their eye as they travel, aside from the dark castle. Giant pillars made of the same material as the Shrines have been raised around it. Thick streams of darkness, the same stuff that Windblight Ganon was made of, coil menacingly over the whole place. Dozens of Guardians, plus other monsters, roam the area, making it extremely dangerous. It looks like it was an architectural marvel, a grand and luxurious citadel of a fortress-palace, before the Calamity.

They could set themselves down out of sight a mile or so down the road from Hateno Town easily enough.