It is hard to find a non-SLR camera that has a fisheye lens capability for the price you state, although quite a few of them have fixed lenses with remarkable zoom capacities.
There are things like the Nikon One, Sony Alpha, Pentax K and Olympus PEN systems, but with lenses you will go as far out of your price range as you would getting a full-blown DSLR, but without the range of lens options.
I would recommend you actually go the DSLR route and spend a few extra dollars. But choose wisely, young Jedi. Once you pick a brand, you are pretty much stuck with it for life, because your lens collection will soon render the price of the camera body a comparative triviality, and the lenses are not interchangeable with other body brands. Personally I like Nikon -- they have higher quality lenses, in my opinion. You can still get the last-generation but still pretty good Nikon D3100 really, really cheap these days, even with one or two lenses and everything, very close to your price range (but a decent wide angle zoom lens and a fisheye will set you back a bit).
Now, for myself, I am looking to replace my obsolete super-compact, which provides lower resolution (but better pictures) than my smartphone, but the choices there are truly bewildering. New products are being introduced at such a furious pace that it is hard to obtain reliable reviews to help with a purchase decision. By the time, for instance, a Consumer Reports review comes out, the highly rated items are often already no longer available, and their direct successors may or may not be as good. In this world, the replacements are often markedly inferior to the cameras they replace in a manufacturer's lineup. Weird. Sort of like the 2012 Honda Civics and VW Jettas.