You have picked the two reasons for not buying a digital camera in that price range.
Most digital cameras have basic audio circuits, which means AGC (automatic gain control) only.
That makes them unsuitable for recording loud live music.
Low light is the Achilles heel of the "point and shoot" camera. The cameras with the better low light performance have very short zooms (about 3X). Even then they do not perform as well as a low cost DSLR (digital single lens reflex) camera.
I suggest you investigate camcorders in that price range.
I'm new around here and I have a question about which one you think is the best compact camera to film live music at the moment without going over budget.
Most cameras from the main brands do a pretty decent job with the image but my main concern is the audio. I've been using a Canon Ixus 980IS and the sound is incredibly good for a little thing like that, with very low distortion even with the loudest bass. But I need to replace it because the sensor is already missing pixels and the lens is feeling its age (spectacular flaring when hit with halogen lights).
What I'm looking for is something with high resolution, a good zoom and keeping that good sound which seems to be asking too much. My main choices at the moment are the Sony Cyber-Shot DSC-HX20V and the Canon PowerShot SX240 HS. I'm currently leaning towards the Sony because I know the DSC-HX9V has a very decent sound quality. Not as good as my Canon (apparently all the stereo mics give more distortion than the mono no matter what) but good enough and the image is great unless the light is very low. Canon is usually better for that.
The choice pretty much depends on which one has the best sound and second but far which one is best for dark interiors. Any other suggestions are welcome as well and if anybody has any experience, please, let me know.