I believe the larger the sensor, the better the camera does in low-light. Less noise. So you'll probably want to shoot for a compact with a larger sensor.
Maybe one of the new Micro 4/3 cameras, as they have a larger sensor than most point and shoots. The compactness depends on which lens you have on it, obviously.
Samsung also recently released a large sensor mirrorless camera. http://www.dpreview.com/news/1001/10010402samsungnx.asp
CMOS compacts with fixed lenses: http://www.dpreview.com/reviews/compare_post.asp
Check the features buying guide to help sort through the different models. http://www.dpreview.com/reviews/compare.asp
I am looking for a digital camera that will work well under low light condition.
Currently I have a Nikon SLR, however, it very bulky and it not practical to carry it in informal setting.
Picture will be used for web, as such resolution is not highest priority. Style, can consistently work well under various condition are more important.
I also looking for an audio recorder, it also used for web, audio quality is not most important. It need to be compact, and easy to get file to web.
Will really appreciate any help.