I’ve got a Nikon P300, which is pretty good. It will occasionally miss focus on occasion. Every now and again, it will refuse to focus at all; I suspect it’s something to do with particular lighting conditions.
Aside from that, I’m pretty pleased with it.
It’s been replaced by the P310, which can be had for around £230 from the looks of it.
There’s tons of choice around though; Sony have some nifty looking ones, but they only had Auto or Manual, not Shutter or Aperture priority as far as I could see.
The Panasonic ones are always popular and generally have longer zooms.
The Canon S100 also looks like a good bet, as does the Olympus XZ-1.
Have you played with any cameras yet? Get yourself along to a large Jessops if not, and have a play with some. You can normally whittle it down to a couple quite quickly once you’ve actually had a play with them.