The Stones of Barenziah are the gems in skyrim, once you locate one stone a Miscellaneous Quest will be added to the Journal, saying that the player must appraise the gem before using it. The stones or gems can be appraised by Maul in Riften and Vex, part of the Thieves Guild, also in Riften.
Find all the 24 stones or gems of Barenziah locations by taking a look at the video(s) below which are only valuable if you get them all. The reward for collecting all of these items is the thieves guild perk, Prowler’s Profit.
Stones (Gems) of Barenziah Locations
1. Solitude, Proudspire Manor: master bedroom (you have to buy the property first: To do this you need to win the Jarl's acceptance by doing sidequests given to you by stewards and have 25000 gold)
2. Solitude, Blue Palace: on a shelf in Jarl Elisif's quarters
3. Thalmor Embassy: In Elenwen's Solar, in a bedroom (during or after the main quest "Diplomatic Immunity") Note: If you did not get this one during Diplomatic Immunity, you can 'glitch' through The Reeking Cave next to the Thalmor Embassy to get back to Elenwen's Solar.
4. Dainty Sload: on a table in the Captain's Quarters (ship is docked between Solitude Lighthouse & Solitude)
5. College of Winterhold: shelf in Arch-Mage's quarters
6. Yngvild: chamber behind the throne in throne room
7. Hob's Fall Cave – necromancer's sleeping area
8. Markarth, Treasury House: next to bed in the master bedroom
9. Markarth, Understone Keep: on a table in a locked side room of the Dwemer Museum
10. Dead Crone Rock: on a makeshift altar in front of the Word Wall at the top of the final tower
11. Whiterun, Jorrvaskr (Companions): In Kodlak's bedroom
12. Whiterun, Catacombs inside of the Hall of the Dead: In one of the wall crypts near a skeleton
13. Whiterun, Dragonsreach: in the Jarl's bedroom area
14. Rannveig's Fast: on a table near the watery prison
15. Fellglow Keep: on a counter in the workroom at the top of the front foyer
16. Windhelm, House of Clan Shattershield: Upstairs first bedroom on the left.
17. Windhelm, Palace of Kings: on a table in Wuunferth the Unliving's quarters (the first door on the left side of the main hall, then at the end of the upstairs hall.)
18. Stony Creek Cave – in the Bandit Wizard's cavern
19. Ansilvund: near Fjori's ghost in the burial chambers
20. Sunderstone Gorge: on the alter in front of the word wall
21. Dark Brotherhood Sanctuary – on the dresser in Astrid's room (must be done during or after DB quests "With Friends Like These" and / or "Destroy the Dark Brotherhood"
22. Pinewatch: Move through Pinewatch until you get to the Pinewatch Bandit Sanctuary. Once in the Bandit Sanctuary defeat 3 bandits in the first room before moving up the ramp on the right. In the next hallway defeat 1 bandit before moving up a flight of stairs. In the next room you will find empty draugr tombs, directly to your right you will see a locked door. Lockpick this door and inside you will find the stone on the top shelf of the right bookcase.
23. Riften, Mistveil Keep: in the Jarl's chambers
24. Riften, Black Briar Lodge: in the upstairs master bedroom.