First list down a list of stuff you want for your camera. Not just budget... as for decent picture quality, all camera gives you that. And as to the acceptance level of the image quality it is basically up to oneself. I find myself having pretty low acceptance level... so even when viewing the 5MP output of my mobilephone, I find those acceptable... but obviously when shown to the experts here, it is not acceptable to them.
Having said that and to make things a little easier, looked to the following models that are on sales these days,
1) Olympus EPL5 (around 4xx, I saw one on sale in the Challenger shop in Jurong East IMM).
2) Olympus EPL6 (going off at around 6xx or 8xx with kit lens. Saw them on sale in the Courts in Jurong East Jem).
3) Olympus EPM2 (if you can find one).
4) Panasonic GM5 (new, small and incredible. But don't know price)
5) Samsung NX mini (good image quality, very small, but only two or three native lenses at the moment)
6) Canon EOS-M (excellent image quality, going off pretty cheaply - significantly less than 1k. Okay AF speed, not excellent and comparable to Oly, Sony and Panasonic cameras).
7) Sony A5100
For compact camera,
1) Sony RX100III (more than 1k though)
2) Canon G7X (7xx at the moment)
3) Canon G1X mkII (more than 1k)