Hi Danny, the Olympus Mju is well regarded although personally I've never used one. I'm very happy with my own P&S cameras which are also made by Olympus: an XA and an XA3. (I also have an XA2 that I got compliments of the aforementioned Hamish, but I'm saving that one for the time one of my other XAs kicks the bucket.)
Actually the XA is a rangefinder that uses an aperture-priority system, meaning you select the aperture and the camera selects an appropriate shutter speed. So,...the XA isn't really a point and shoot but its very small so it seems kind of like one. The XA3 on the other hand is much closer to a point and shoot since it has automatic exposure and you only have to select one of three distance options for focus.
Both of these cameras are capable of cracking images, as are their brethren the XA2 and XA4. There also happens to be an XA1, which is lowest on the XA food chain and therefore can be had with the least expense.
XA prices seem to be climbing. You could probably pick up an XA2 or XA3 for $30-50 US. An XA is liable to set you back $50-90. An XA4 is the most expensive, with current prices creeping up to and over the $200 mark. The XA1--not to be confused with the XA--should be the cheapest at around $20 I would guess.
Of course, any of these might be found in a charity shop some day for a few dollars,...but I don't usually get that lucky.
On balance, if you want fully automatic P&S capability, the Mju might be the best combination of quality for price, size and ease of use.
Good luck!