Look at some GOOD review sites. Use the parameter selectors on such sites to select what you value most.

One of the best is DPREVIW

Also well spoken of although somewhat less formal and more "chatty" is Steve's Digicams but there are many others.

Few major camera review sites are going to be scathing about cameras from major manufacturers - they rely on getting future access to cameras. This is not to say that they are biased - just that to some extent you must "read between the lines". Choose sites which are either recommended by knowledgeable people or ones which have an at least moderately analytical and logical approach. There are surprisingly many camera reviewers who seem to know very little of real worth.

To start, look at this group review, see what you can get for the money, and then perhaps refine your question. his is a June 2010 test and at that date prices were mostly in the $200 - $300 range. There will be newer models now but this gives you a good starting point.

Compact travel zoom group test

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Notes:

DSLR?: Good low light performance and low cost are not impossible but do not usually go together. Even an old and low spec used DSLR will usually ot perfom a top spec point-and-shoot for low light photos and it may be worth looking at second-hand DSLR if size, weight and age are not unacceptable issues.

Megapixel madness: Generally more megapixels leads to more noise and worse low light performance. Nikon's 36 mp D800 shows that this does not have to be true, but as a general rule, more mp is not a formula for better performance in most areas other than pixel resolution. A 6mp camera can produce very fine photos indeed - something which is beginning to be forgotten in the race for ever more pixels.

High ISO madness: Having higher ISO settings by itself does not lead to better low light photos. What it does is allow a faster shutter speed for a given amount of light. The faster shutter reduced blur due to handshake and due to subject movement. But using a higher ISO setting also leads to more noise. Handshake blur can be greatly reduced by learning how to hold a camera steadily (an art in its own right) and by bracing the camera and/or your hand against a solid object. Subject movement is harder to compensate for. Consistent smooth motion can be dealt with to some extent by "panning" - moving the camera to track the subject, but when different parts of the subject move independently (such as a person dancing) then a faster shutter speed is the only solution.

Flash helps immensely, but it will often not be possible or appropriate. If using flash be aware that if a low shutter speed is used the photo will often include significant amounts of light from both ambient lighting and from the flash. This can lead to a sharp image from the flash AND ALSO a halo image around the sharper image consisting of more blurred and spread lighting due to ambient light. This can be a useful visual effect, but if it is not wanted then use a faster shutter speed or smaller aperture.

If no motion is involved then a tripod or informal camera support vastly improves low light shots.