The reason why you usually get blurry pics is that the camera chooses to low of a shutter speed.
Avoid Nikon's - they really, really love low shutter speeds.
Canon's are better, but not perfect.
The only way to really avoid blurry pics is to get a camera with manual controls and set the shutter speed yourself (or get a camera where you can set the minimum shutter speed to at least 1/60 - unfortunately I don't know of any non-dslr's that can do that).
The Canon sx230 lets you set the shutter speed manually, and costs around $230. It's a camera with a lot of optical zoom.
The Canon s100 is more expensive - $360 - and it's better for taking pics in low light (though it doesn't zoom as far). Also has full manual controls - it's what I own.
I'm sure you'll say "she doesn't want to have to set anything manually", but unfortunately I don't know of anything to specifically recommend who's auto mode is perfect for non-blurry pics.
I do think that any modern Canon compact will give you a lot less blurry pics than a 5 year old Sony model.