Some prices, from B&H:

Panasonic LX7: $448
Panasonic LX5: $398 (on Amazon: discontinued at B&H)
Canon S110: $449
Canon S100: $280 (on Amazon: discontinued at B&H)

Panasonic GX1 (kit including basic zoom lens): $449/$559 (more if you want the lens that collapses into itself when you turn it off)

Sony RX100: $648

Basically, you pay a huge premium for the Sony, but it's a remarkable achievement of packaging so much into so small a case. Conversely, the older Canon S100, still new-in-box, seems to be quite the bargain.

You said you're willing to go used. B&H is offering a GX1 body plus the 14-42 lens (rated 8/10 on their quality scale) used for $319. That might be attractive to your budget.

If you do get the GX1, you have the ability to buy other lenses, which opens up opportunities you won't have with the pocket-sized cameras. Just make sure you budget for clear filters to put in front of your lens, such that the filter takes the hit rather than your lens. A Tiffen 52mm "UV" clear filter is $5. The über multicoated version of the same filter from B+W is $31. In either case, the purpose of the filter is to "take one for the team". You'd rather have to replace a damaged cheap filter than a damaged expensive lens.