My first question is, what type of smart phone (if any) do you carry?
In that price range, most of the options aren't far superior to the better smart phones (iPhone 5, Galaxy S, etc). The main advantage of the traditional p&s being optical zoom. And if that's important to you, you can get an awful lot of optical zoom for $200. The main advantage of the good smart phone -- high definition touch screen, in camera editing, wifi sharing, etc, etc.
If you don't have a smart phone, and/or optical zoom is important -- the Canon sx260 is one of the better compact super zooms, it's around $200.
The Nikon p310 is just under $200, and it has a fast lens.
The cheapest good compact I've seen is the Panasonic lx7-- slightly larger sensor with a very fast lens. Seen it as cheap as $320.