It may be a side-effect of the way I play, but I usually meet Kharjo at the camp outside Dawnstar, and the Moon Amulet always seems to be in Frostmere Crypt. I assume this implies that the Radiant system prefers the nearest match when making a "random" selection of location.

I think the reason he's always at Dawnstar when i start it, is that at the Riften end of the route, he's less conspicuous, and they travel too fast to stop them in between.

What is everyone else's experience with this quest, in particular, where have you been sent to retrieve it? I'd expect a few local to Riften, but any in the West?