If I shine a bright light on a neutron star, what would it look like? If there are no orbitting electrons in a neutron star's makeup to interact with EM, what happens to light that strikes it?  
 A: A neutron star would shine brilliantly with its own light for a very long time indeed*, especially if it were being heated by matter falling onto it. The emitted light would be dominated by blue, with decreasing intensity towards the red end of the spectrum. The net result overall is bluish white, but not a perfect blue mixed with a perfect white.
But you specifically want to know what a neutron star's incident-light properties are? That is much more difficult to answer. Because a neutron star is so dense, only its outermost layer is going to matter to its optical properties. A neutron star has a thin atmosphere of extremely hot gas, but due to the extreme surface gravity, it will only be about a meter thick. Neutron star atmospheres are currently an active area of research. I'm not sure if that is enough to be opaque ala Venus, or if the true surface would be visible.
In any event, in the top layer of the crust, the density drops below the neutron drip density and the nuclear saturation density, so the composition will have the normal distribution of precisely equal numbers of protons and electrons, which will probably be approximately equal to the number of neutrons. The reflective properties will therefore be like hot, ionized iron, helium, or hydrogen, depending on which is actually present.
*White dwarfs are cooler than neutron stars and have a larger surface from which to emit radiation, yet even their cooling time scale is longer than the age of the Universe. Unless I'm missing something important about a neutron star, a neutron star should be much much hotter than the surface of a normal star for as long as you could possibly care to watch or wait.
A: It should be reflective, since the crust of the NS is not made of pure neutrons (even the interior has some non-negligible fraction of free electrons), and the "normal" matter should be highly ionized, thus conductive.
Re: the extreme thermal brightness of a million-degree black body, you could still see the visible light if you shined a coherent source like a laser. Also, very old NS's cool off below that temp, but they are much harder to find.
A: I think, honestly, it would look like a glass ball or a concave mirror with flashes of light where matter gets sucked in. A neutron star would have significant gravitational lensing. I don't think the surface itself would reflect any light, even though it's guaranteed to be the smoothest surface imaginable.
A: The details of what the surface of a neutron star would look like is poorly understood, involving lots of poorly understood physics. However, shining a light on it is going to be tricky since the radiation temperature of the surface of a neutron star is about a million degrees Kelvin and, even in visible light, would be hundreds of times brighter than the surface of the Sun. 
