Here's the locations of all the Stones of Barenziah, needed for the 'No Stone Left Untouched' quest.
1. Search the Jorrvaskr in Whiterun. Find the stone in Kodlak’s room.
2. Search the Hall of the Dead in Whiterun, then enter the Catacombs. Check the wall crypts to find another stone.
3. Find the stone on the Dainty Sload, a boat docked in Solitude. Look in the Captain’s Quarters, on the table.
4. Enter the College of Winterhold and search the shelves of the Arch-Mage’s Quarters.
5. The stone can be found in Yngvild, a cave north of Winterhold and east of Dawnstar. Search behind the throne to find a chamber containing the stone.
6. Another stone located in a cave, called Hob’s Fall Cave. Search the area between Dawnstar and Winterhold. You may come across a lighthouse, search east of Frostflow Lighthouse. The stone is inside the Necromancer’s sleeping area.
7. Find a stone in the Treasure House of Markarth, search the master bedroom to find the stone.
8. In Understone Keep, in Markarth, look for a locked door into a side room of the Dwemer Museum. The stone will be inside, on a table.
9. An undead gathering place called Dead Crone Rock can be found southwest of Markarth. The stone can be found on an altar near a Word Wall at the top.
10. Found in Proudspire Manor, of Solitude. You’ll find the stone in the master bedroom.
11. Found in the Blue Palace, in Solitude. Look in the Jarl’s quarters, on one of his shelves.
12. Inside the Dark Brotherhood Sanctuary, look in Astrid’s room for the stone.
13. The stone can be found in Thalmor’s Embassy, while completing the “Diplomatic Immunity” quest for Delphin in Riverwood. While in the embassy, look in Elenwen’s Solar.
14. While in Dragonsearch, of Whiterun, explore the Jarl’s bedroom to find a stone.
15. In the wilderness, you’ll find a dungeon called Rannveig’s Fast northeast of Rorikstead and southeast of Marthal. Look for a prison area, and search the nearby tables for the stone.
16. The dungeon of Fellglow Keep can be found east-northeast of Whiterun. Look on the counters of the workroom to find this stone.
17. Check the House of Clan Shattershield in Windhelm, simply search the first upstairs bedroom to your left to find the stone.
18. Inside the Palace of Kings in Windhelm, look on the table in Wuunferth the Unlivind’s Quarters.
19. A cave called Stony Creek Cave can be found north of Ansilvund, southeast of Windhelm. Look in the area where you encounter the Bandit Mage.
20. Ansilvund, in Eastmarch, contains a stone near where you encounter Fjori inside the burial chambers.
21. Simply search the Jarl’s Quarters of Mistveil Keep in Riften.
22. Search the master bedroom of the Black Briar Lodge, the one outside of Riften.
23. Find Sunderstone Gorge south of Gjukar’s Monument and north of Moss Mother Cavern, in Falkreath. You’ll find a Word Wall inside, with the added bonus of a nearby stone.
24. A farm called Pinewatch can be found northeast of Falkreath. Inside the farmhouse, look for a secret entrance into an underground cave. Inside the Bandit Sanctuary, look for a locked door. Lockpick the door, inside you’ll find the stone on a bookshelf.