I'm actually interested in the topic verbatim here (I know there have been other P&S threads). I need to update from my wife and my 8-10 yr old college P&S cameras. Many of my friends are getting SLR cameras but don't really know how to use them to their full potential. I'm in the camp that I'd like a nice "daily driver" that I can pick up from time to time and take high quality pics without all the hassle of adjusting 20 settings to make a shot look good. Aka, point-and-shoot. I haven't looked too much, and I don't have much/any camera knowledge, but I'm fine with something 10x optical or less since I favor low-light quality over optical zoom. Let's say....roughly $300?
Canon S110/S120, on sale. The main issue here isn't the 'settings' or the 'zooms', but rather just how large of a sensor you can get, and just how fast of a lens (maximum relative aperture, in f/ values, lower being better). The larger the sensor, and the wider the aperture (lower f number), the better in low-light, generally speaking. This is why Sony's RX100 series has garnered so much attention, though they are too expensive for most.
However, if you're up for learning photography (and there's like five critical ideas at most), a DSLR and kit lens will utterly destroy any available point-and-shoot across the board, as would a Micro Four-Thirds kit or Sony/Fuji mirrorless kit, supposing you found one that met your budget, as they all have larger sensors and faster (relative) lenses than P&S cameras.
Consider my suggestions in the first paragraph if you're really prefer to keep it simple; but in the span of maybe an hour, I could have you shooting manual with just about anything that supports it, from turning the camera on to posting a processed shot on Facebook, and it only gets faster from there. The processes behind photography are cake for any technically minded person.