The Honorspren got an entire vault of perfect gems full of Stormlight, so I agree with Inquisitor and think that's where they are.
How the spren got hold of them is a completely different topic, though. I wouldn't be surprised if they worked together with one of Roshar's secret organizations (or even the Ghostbloods). And now it gets interesting imo, what's their reason for accumulating all these gems? Is it only wealth? I don't think so.