Assuming solar systems similar to ours orbiting a massive black hole (similar to the one in the movie Interstellar) then you would have some effects, a lot which would depend on how close you are to the black hole itself. For the solar systems to remain stable over eons of time, they will need to be orbiting at a great distance (with a period measured in thousands of years).
The night sky would actually be rather similar to what we see here on Earth, until you look in the direction of the black hole itself. The black hole will be noticeable because it will bend starlight around itself forming an "Einstein ring", which will be pretty mind bending for even primitive priests and shamen doing unassisted night sky astronomy.
If the black hole is active, then things will be even more exciting from a visual perspective. Infalling matter will tend to orbit around the black hole at ever increasing speed. As the matter accelerates it also heats up, eventually becoming a visible disc of matter (and even energetically emitting high energy radiation.) If the infall is great enough there might even be beams of radiation coming from the poles of the black hole.
The last effect will be gravitational lensing, which will occasionally bring different distant objects into focus. The various solar systems might actually become briefly visible as they pass in the focus of the black hole (this is related to the Einstein ring, and you will not be getting a "naked eye" view of the other solar system, but a telescope will be able to make out more details as the other solar system or object passes into the focus of the gravitational lens).
So there will be some visible effects, but not as spectacular as you might see in a Hollywood movie.