(With thanks to Broadway Camera.)In your hands, the construction is fairly high quality. It looks like a matchbox compact, but it's metal construction keeps it in fitting with cameras like the Canon G-series. It's not quite as solid and heavy feeling as the Fujifilm X10 or X20, and it's a tad bit bigger. However, the finish of the metal has a nix satin-like texture and the placement of the rear thumpadmakes holding the camera comfortable given its small size. In fact, if nobody told you that an APS-C sensor sat inside the housing, you would never guess that was the case. The design looks fairly minimal, but it is functional and to the point.
Operation and controls work like you think a Nikon would work, so there is a family resemblance. That's a good thing if you want one as a satellite camera to your Nikon dSLR, keeps the brain space tidy. If there is a difference in image quality between this and either the D7000 or the D5100, I couldn't tell, so for the most part, it will give you more or less the same or similar looking pictures. I don't know if the exposure metering or default tone curve of the JPEG output has been changed, but I doubt that's the case. Since it was a new camera, I only had access to the JPEG's, but I would say that they are electronically corrected for lens distortion and vingetting, since you don't see much, if a all, in the out of camera shots. Sharpness across the frame is what you would expect with any Nikon 16mp DX camera and a good quality lens at 17mm. (Want to make a group of jaded photography professionals break out in laughter? Start shooting at a brick wall in total seriousness to "test" the lens. Good laughs all around.)
Speaking of which, the Cool Pix A does not have an optical low-pass filter, like the D7100. The images don't have quite the same "wow!" factor because you also aren't getting the added benefit of more resolution, but they are sharp. I think Nikon did a poor job of headlining this feature, there was some confusion at launch time about whether it had it or not.
Speaking of the focal length, this is a problem for me with this camera. The lens, at 17mm (or roughly 28mm FX equivalent), is a good compromise if you want an all-around lens that isn't too expensive to build, but it's also a compromise for composition. For wide-angle, 24mm is more exciting, but less useful for all-around shots. For all-around use, 35mm is still the classic street-photographer focal length. At 28mm, the shots will get everything in for the most part, but it will take work to generate compositional strength or variety. That or you will need to do more cropping than you are used to.
Focusing speed is also a bit Nikon-like... Nikon Coolpix-like to be exact. It's not going to matter if you are a single-shot snapshooter, but there is a noticeable difference between this and the Fujifilm X20, which has on-chip phase detection, and it's miles slower than the Nikon CX cameras.
It's also way more expensive than a camera this size. For the same price, you could buy a D7100 body, or a D7000 with a lens. So just like the Sony RX models, you're paying for small size, but unlike Sony, they didn't hit the right price point in my opinion. For this price, there would have been much more positive buzz if it had the same sensor as the D7100, and it wouldn't cost Nikon that much me in component costs since it would be sharing production economies of scale with a high volume camera. Nikon can charge $599 USD for the same sensor, phase detection autofocus and a lens when it's packaged in a D5100. So therein lies the problem... you would expect a new product, as well as premium products, to have something of a price premium, but when the amount of pricing premium is this visible, it can turn off the consumer. (Look at the price that Canon is charging for their APS-C compact, the EOS-M...)
The last problem is the camera sitting right next to it on the shelf, the Fujifilm X100s, which retails for only $100 USD more. You pay slightly more, but you get more. You also get Fujifilm's handling, menu and control quirks, but the slight price difference is well worth having phase-detection autofocus, the added bite of the X-Trans sensor, and Fuji's excellent hybrid optical viewfinder. That said, these are two completely different cameras: the Nikon is definitely the size champion if size is the first thing that you want to cross off your list.