It's mid-morning.
My thought was that it's perhaps a mile or so outside of Edoras, and happens to be an old, old Numenorean ruin right back against the mountain, hidden in a copse of trees (if a copse is big enough). To Numenoreans it would have been quite humble, and to an Eorlinga like Thornden rather impressive but very, very ruined and very, very ancient. To a Hobbit, BIG! To a boy, the stuff of dreams, no doubt!
If you've ever been to England, it's on a para with the old, old standing stones that are scattered throughout the island, except it's not standing stones, just 'that old', and the mouldering remains of an old way-station. Yeah. That's it. .... thus it would be no great surprise that a similar "way station" such as Edoras would be begun within a few miles of an ancient one. The lay of the land makes it suitable and all that. At least it's plausible, eh?