What is a higher priority, zoom or low light?
My DW uses the Canon SX (she has the SX210, but you may want the more up to date SX260). It's packed with features, takes good overall shots, its very compact, with a 20X zoom. And it's $289 on
Amazon. It is a very versatile camera, that will suit the needs of most people.
Alternatively, if you are looking for higher quality portraits, a better ability to shoot indoors without flash, better low light performance... You can look at the Canon S95 or S100. You don't get the zoom, but you do get a superior lens, which will offer better overall performance. Both cameras will run more in the $300-$350 range.
Another good option around $300 is the Sony Cyber-shot DSC-HX5V, with a 10X zoom, and tons of features packed in. The lens isn't as good as the Canon S100, and the zoom not as good as the SX, but it is does make up with a lot of useful features. And I believe the Sony shoots a bit faster, and allows for a slower shutter speed.