The hidden Vault-Tec Bobbleheads can be found at the following locations. Collect a Bobblehead to gain +10 to a skill or +1 to a stat.
Agility: Greener Pastures Disposal, in the small office covered in radiation.
Charisma: Vault 108, in the Cloning Lab.
Endurance: Deathclaw Sanctuary, at the entrance on a table next to a rotting Brahmin corpse.
Intelligence: Rivet City, on Dr. Li's table in the Science Lab.
Luck: Arlington Cemetery North, in the basement on a shelf directly below the stairs inside the house to the north.
Perception: Republic Of Dave, on a bookshelf on the right in the Museum of Dave.
Strength: Megaton, in Sherriff Lucas Simm's house.
Barter: Evergreen Mills, in back of the Market Bazaar on a shelf in the upper-right side behind the Raider Trader that does not attack.
Big Guns: Fort Constantine, in the basement of the CO Quarters inside a safe in the wall.
Energy Weapons: Ravenhold
Explosives: WKML Broadcast Station, turn on your local map. Go through the doorway to the sealed cistern to find it.
Lockpick: Bethesda Ruins, in Bethesda Offices East, on the top floor near the door to the bridge.
Medicine: Vault 101, on your dad's desk when leaving.
Melee Weapons: Dunwich Building, just before you leave the Virulent Underchambers, on the floor next to the door.
Repair: Aerefu, in Evan King's house.
Science: Vault 106, from the living quarters, enter the room all the way in the rear left corner. There is a room with a bookcase lit by a bright light. Search the middle (toward the right) of that bookcase.
Small Guns: National Guard Depot, go through the training room and offices to exit from a door to the main room. Use the power switch on the wall to your left, and enter the Armory door, then search the shelves.
Sneak: Yao Guai Tunnels, on top of a metal box in the Den, on the right of the map near some water.
Speech: Paradise Falls, on a table inside Euology's pad (Slave Master's house).
Unarmed: Rockopolis, go directly west from Casey Smith's garage. Look for tattered banners that are strung up. Use your local map to find it.