Your understanding is correct.
There cannot be a geostationary satellite at the poles, basically because it would have to be at rest, which cannot happen as it would get pulled by the earth's gravity and eventually crash to the surface.
In fact, there cannot be a geostationary satellite anywhere else, except above the equator(in an equatorial orbit). This is fairly easy to prove.
Imagine that you wanted a satellite directly above the place where you are right now, lets say 500 km away. Now we know that the earth is rotating, so the place 500 km directly above you will also move in a circle.This circle has its center somewhere on the rotational axis of the earth(Not necessarily coinciding with the center of the earth).
If you want your satellite to move on that path, It will require a centripetal force continuously acting towards that center. Now if a satellite is purely under the influence of earth's gravity, there is a force acting on it directed towards the earth's center. Now if this force were to act as the centripetal force for the motion we want for our satellite, the orbit's center would have to coincide with the earth's center, leading us to the fact that a geostationary orbit has to necessarily be an equatorial orbit!
P.S. I'm sorry I couldn't provide you with a 3D diagram, but Wikipedia has a great diagram for a geostationary orbit: