Starlight Interstellar Theater (4 Star Cores)
Fallout 4’s Nuka-World expansion tasks players with seeking a lot of different items, usually for great reward. One such quest, called Star Control, has players seek out Star Cores. While only 20 are needed to complete the basic quest, finding all 35 will get you the Quantum Power Armor.
After entering Starlight Interstellar Theater, head straight and keep to your left. There will be a broken down bathroom with a hole in one of the walls. The core is right on the ground in that hole.
Head out of that bathroom then head left. You’ll find yourself in a theater full of little rockets. In the back is a control panel with your second Star Core.
Turn around and walk back towards the theater screen then take the door to your right. You’ll see an elevator with a hallway to the right of it. Go down that hallway and make a left into a sort of rest area. The next room has a control panel with another Star Core.
Head back towards the theater, but make a left before entering and head down the hall towards an elevator. Take the elevator up and you’ll find another Star Core in a control panel.