feedmec00kies isn't asking for a camera that will shoot as well as a digital SLR, but a camera that will take better low light, flash-less, close-up pictures than what most point and shoots currently available will take.
This shot was taken in a low-light (though not very low-light) setting, was flashless, and was a macro shot. ISO was 400.
Here's another one.
And I think this picture is a pretty good example of what a point and shoot can do (unfortunately, the properties of the picture aren't available for viewing).
Are they as good as what you can get with a digital SLR? No. But are they good enough for what most people are using their digital cameras? I think so.

(Err, assuming you were saying that to me, and not that I was the poster talking about looking for a camera...)
I looked at the photographs, though, and did some calculations for shutter speed because I doubted they were hand-held. Take the
first photo, for example. Looking at the EXIF data, it says the shutter speed is "529/100". I used the explanation from
this page to convert the value to the shutter speed in seconds...
Shutter speed by APEX value. To convert this value to ordinary 'Shutter Speed'; calculate this value's power of 2, then reciprocal. For example, if the ShutterSpeedValue is '4', shutter speed is 1/(24)=1/16 second.
...Using my meager math skills, I found that the shutter speed is 0.0357 seconds.
The
second photo has a longer shutter speed: 0.0692 seconds.
I decided to compare it to the
the only macro+low light photo I have, which happens to be in a similar lighting condition as the first two. The shutter speed is 1/13 seconds (0.0769 seconds). I know that photo was taken in ISO 800, because it was taken when I first got my Canon Powershot S3 before I realized how much grainier photos became in the higher ISOs. I can see particularly in the bottom left corner. Maybe it is good enough for the usual user. I probably have very high standards. But I still see it as problematic. For photos of food for your own records, or for a 72dpi photo on the web, it's probably fine.
(BTW, there was no EXIF data for
the third, but I'm not sure whether or not it was taken with the camera hand-held.)
FWIW, though, there is actually a pretty small degree of variation between the compact cameras on the market. A lot of it has to do with sensor size. Buy one that is generally highly recommended within the price range you're looking for, with the features (like manual settings, view finder, optical zoom capabilities) that you want. The previously-mentioned Fujifilm seems to be highly recommended specifically for it's low-light features, but I don't know much about it because I prefer to own a very well-rounded camera that allows for full manual control, rather than just something with more low-light capabilities.