My recommendations:
<$200: Canon SX130IS
<$300: Nikon P300
<$400: Nikon P7000, P7100, or Canon G12
<$500: Olympus XZ-1
For the specific cameras I mentioned, they include manual exposure controls, fast lenses, and a couple of them even have manual focus capability and customizable white balance, not something normally seen in a compact camera.
Skip mirrorless cameras - such as the Sony NEX, Olympus and Panasonic Micro Four/Thirds cameras, or the new Nikon 1 cameras (will be available soon). They cost almost as much as a DSLR system once you buy a few lenses, and unless you really need a small format, they are not cost effective.
Also skip bridge cameras (Canon SX30IS, SX40IS, Nikon L120, P100, P500, and especially the Fuji S2950) as they suffer from the combination of higher than necessary MegaPixel count sensors and ridiculously high power zoom lenses. The overkill in these two areas serve to reduce photo quality.
There are two Myths surrounding compact cameras - and bridge cameras in particular:
Myth #1. The more MegaPixels the better the photo. While the photo has a higher resolution, the low-light capability suffers, mostly in the form of noise. Also many compact cameras do not have sufficient processor speed to quickly process such high data rates, so you can end up with horrendous shutter delays. For compact cameras, 10Mp is ideal, 12Mp is maximum.
Myth #2. The higher the zoom the better. There is no such thing as a perfect lens, and the higher the power, the more compromise. For lenses 4x is ideal, anything above 7x is going to have optical issues, as there will usually be un-sharp areas along the lens's focal length.
Compact camera lens comparison: http://www.althephoto.com/lenses/digital-zooms.php