Stats
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.
Skills
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.
When you've spoken with her, go into the house marked Common House and speak to a man named Pappy. There should be a speech skill dialogue option that says "You came here with Bittercup, right?"
Every time you click the speech you will get a certain amount of XP. You can keep clicking until you have enough XP.
Note: This trick requires you take the "evil" path. After agreeing to help Mr. Burke nuke Megaton, go into every single house and steal everything (any little piece of junk you can carry). Sell them to the local shops (Craterside Supplies,
Get to Andale (south central part of the map)
Wait until around 1am and go into the Smith house while they are sleeping.
Go upstairs into the kid's bedroom and use sandman on him (crouch and select him and and use the first option). This will give you XP.
You can repeat this (using Sandman on the kid) to gain infinite XP, increasing the difficulty if you want to gain more XP faster.