In reply to Phil Payne:
Thanks for all the replies. I just went out again and ended up buying a Canon Ixus 230 HS. Apparently the HS stands for High Sensitivity and it uses some sort of back-lit CMOS sensor for improved low light shooting.
Having had a play with it in the shop, it was definitely easy to use and the full auto mode seemed to work really well and the controls are nice and simple to operate. I would have gone for the Ixus 500 HS, but decided that the touch screen would probably be too tricky for my mum.
Someone mentioned the Lumix LX7 and that looks like a great little camera. I'm very tempted to get one of those for myself as a bit of a Christmas treat to myself.