There are some extremely capable Point & Shoot cameras out there now... I suggest a trip to a store that has a display with working models. Maybe even take your own memory card with you and play around in the display.
Just know that P&S cameras have small imaging sensors, which means the pixels are smaller and more dense... this contributes to noise and lack of detail. That is why images from Digital SLRs are much cleaner at high ISO. Larger photocells on the larger imaging sensor.
You need to determine what your "real" financial limit is and what results will work for you.
And, have you ever considered taking up photography as a hobby?
You mentioned that you want the camera to be "very automatic" but have you given any thought to whether or not you'd like to have a simple "camera" or a photographic tool? Getting into photography is not the same now as it was back in the 80's. Do you mind looking through the viewfinder instead of the back of the camera? Even with a budget of only "a few hundred" it is now possible to buy a very, very capable DSLR and take publish grade images. (Geez, I sound like a salesman)
There is a tremendous amount of great, cheap gear floating around for sale right now due to the explosive manufacture of new models in the DSLR segment. The groundbreaking camera models from just three or four years ago (like the Canon Rebel) are now available at greatly reduced prices. In some cases, a third or a quarter of their original cost. Each generation of new gear that is released drops that value further...
Here's an example of an 8MP Canon Rebel, It has the same sensor in it as my Canon 20D (from which I've made clean 20"x30" prints). It is the second generation of the Canon rebel and sold new with a 18-55mm lens for around $900. This one appears to be in great shape and has the more desireable Image Stabilized version of the lens (worth over $100 by itself) for a $345 Buy It Now, and it even includes free US shipping. [ebay]110432964197[/ebay]
If a DSLR is too big for your tastes, then check out this small frame Panasonic Lumix 12MP that a good friend of mine is selling:[ebay]260474058721[/ebay] This is a much newer style camera, and won Popular Photography's CAMERA OF THE YEAR last year because it is much smaller than a standard DSLR, but offers much of the same performance. This one does not have an optical viewfinder, instead it has a digital view finder or the articulating screen on the back. He paid $800 for it about nine months ago, now he's selling it with some extras for $550. That might be more than the few hundred you mentioned, but I bring it up because I know the seller and he is good people. With that said, he is selling it because he started taking photography seriously and has moved to a Nikon D90 system.
But, even the DSLR's from several years ago take cleaner high ISO images (which you will need in low & medium light) than any current P&S camera will. Larger sensor=larger photocells=Lower noise=more resolution. It's not just about megapixels. I'll put my 8MP Canon 20D up against any 12MP P&S at 800 ISO.
So..... I say step up to a used, older DSLR and you'll be making an investement into a photographic tool rather than just buying a camera.
Models worth checking, which may be available in that ballpark:
Canon Rebel XS
Canon Rebel XSi
Canon 20D (small 1.8" screen, but fantastic value. magnesium frame)
Canon 30D (basically the same as 20D, but larger screen and thus a bit more $$)
Nikon D40
Nikon D60
A great resource for camera comparisons:
http://www.dpreview.com
Good luck!
Canons produce some of the best image quality and they have a number of models you can get from $100 to $200 on sale. A great source of information and hands on testing with sample pics is 
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