As mentioned, you may have some issues with the "new" criteria, except for some Japan-only Fuji P&Ses, although you may also be able to find some Olympus models as new old stock.
I've played with a few of these. My current favourite is the Canon Sure Shot Classic 120 - although technically it doesn't have matrix metering, supposedly it's pre-programmed with a wide variety of lighting conditions it selects from, and generally exposes very well. Also one of the few cheaper ones that has the option of +/-1.5 EV (although that deactivates the flash). Also I quite like its Portrait and Macro modes - they generally do a good job for portraits. The main downside is that the zoom/focus motors aren't the quietest, so may startle/alert people that you're taking a picture if you're trying to be subtle. It does start up quickly.
Other P&S/small 35mm cameras I've tried:
- Olympus XA: I like the size and the clamshell, however the rangefinder spot is very small, and I've had issues using it in room light. Also, somehow I managed to break one while flying to Vegas - still not sure how, as it was in my carry-on and not dropped. I seem to be in the minority, here, though.
- Olympus Stylus Epic: Easy to use. No real complaints about functionality (aside from the settings reset as mentioned above), except I had some issues with red eye due to the position of the small flash. Another P&S that managed to break somehow on my trip to Vegas. Once again, it seems to be me and not the camera
- Olympus Stylus 120: Zoom version of the above. Good results. My only complaints are that there is sometimes noticable lag between pressing the shutter and the actual picture being taken, and it seems to default to a slower shutter speed instead of opening the aperture for more light, which can lead to some shake/blur.
Ideally I would like something with the features and quality of the Canon, but quieter, and one that doesn't cost a tremendous amount. I've heard good things about the Japan-only newer Fuji P&Ses, but I'm unwilling to pay the prices for them.