7 star cores are scattered throughout the location:
One in a control room just to the right of the boarding platform.
One is part of the second Nuka-Galaxy control terminal, just after the first big room filled with asteroids.
In a computer terminal right before the battle between robots, and just after using the working lift.
After going through the hallway with robots fighting animatronic aliens, there are a lot of stairs. Going up these stairs and into the next hall, there are stairs on the left. On the top of the stairs is a computer with a star core, to the right of the skeleton lying on top of it.
In a terminal at the exit ramp.
Between the exit ramp and the boarding platform is connecting hallway with master locked doors. Going up the stairs behind any of the two ends up in a control room. One star core can be found here.
In a room adjacent to the above is the last star core.