As a Nikon DSLR shooter, I can say with confidence that.. I'd stay AWAY from Nikon point and shoot camera's like the plague ! They're just awful, which is really a shame. Seems they don't invest enough of their R&D money into their portable market.
I've only ever owned and loved Canon point and shoots, and a bridge camera (S3IS), and can say with certainty that you can not go wrong with a Canon. I bought my wife the Power Shot A590IS and I probably use it more than she does. It is able to be used with manual controls such as aperture, shutter speed and ISO, so if you have a lot more control vs full Auto mode, which is great if you're shooting at night and have a very light tripod..
Auto mode also works quite well, so can't complain there. The only thing I don't like is that it seems to be an battery eater. Always carry spares..
Now, other than Canon, I would seriously consider a Panasonic alternative in the form of the Lumix DMC-ZS1, ZS3 or ZS5. The main differences between the three, which differentiate their prices, is the quality of the video. All of them zoom while focusing, which is very rare in a point and shoot, and image quality is great due to the Leica lens. Which mind you is capable of a 12X optical zoom, NOT digital.
This will allow for a really nice depth of field when zooming in on a subject, blurring the background. The most expensive model which tops out at your desired highest price range ($300) is the S3 The S5 is $258 and the S1 is $189
Panasonic | Lumix DMC-ZS1 Digital Camera (Silver) | DMC-ZS1S
Personally speaking, I don't think you can go wrong with the ZS1. If you want better video quality, then you spend more for either the Z3 or Z5.
Going down the Canon road, I'd seriously have a look at the SX 120. It also has a 12X optical zoom, and manual exposure capabilities for those times when you want more control over your photos. It gets great reviews, with the only negative being that there's a slight delay between shots when using the flash. Oh, and with this camera, the flash doesn't automatically pop up. which is a good thing. It gives you the option to use flash when you want to, not when the camera wants to. This is not a negative.
Canon | PowerShot SX120 IS Digital Camera | 3634B001 | B&H Photo
One last thing. Do not be fooled by megapixel numbers. They are absolutely worthless to boast about on a point and shoot. In fact, the more megapixels, the more you should be wary of the image quality. The problem is that these camera's have extremely small image sensors, and the more pixels you try and cram on to them, the more processing the camera has to do to compensate for digital noise. You don't want that. My 6MP Canon produces image quality far better than most if not all 14MP point and shoots.
The main point to more megapixels is concerning how large you're able to blow up a print. Technically speaking, the more MP, the larger the print you should be able to get. But trust me, a 14 MP P&S will introduce artifacts which you'll see if you try to print at a very large size.
/rant.