24 player.moveto locations to the stones of Barenziah + Crown on Skyrim.

The Elder Scrolls V: Skyrim (Photo credit: Wikipedia)

If you find an Unusual Gem while questing, you'll prompt a miscellaneous quest urging you to get the gem appraised. Once you do so, by taking it to Maul, Vex, or any members of the Thieves Guild in Riften, you'll find out that there are 24 gems total, but they're only valuable as a whole set. Most of them are found for doing extra jobs for the Thieves Guild. For finding all of them you get a perk called Prowler's Profit that increases your chance of finding additional gems in chests. Woot.
After the cut you'll find all 24 Stones of Barenziah locations in Skyrim.
You will find Vex at player.moveto 00028938

1. player.moveto 0007F956 or Search the Hall of the Dead in Whiterun. In the first room of the Catacombs on the left wall near a skeleton you'll find a stone.
2. player.moveto 0007F923 or Search the Jorrvaskr in Whiterun, you'll find a stone in Kodlak’s room.
3. player.moveto 0007F965 or In the House of Clan Shattershield in Windhelm, you'll find the stone in the first upstairs bedroom to your left.
4. player.moveto 0007FB65 or North of Ansilvund and southeast of Windhelm you'll find a cave called Stony Creek Cave. You'll find the stone in the Bandit Wizard's cavern.
5. player.moveto 0007F962 or In the Palace of Kings in Windhelm, you'll find the stone on the table in Wuunferth the Unliving’s Quarters.
6. player.moveto 0007F927 or On the Dainty Sload, a boat in Solitude between the Lighthouse and Solitude check out the Captain’s Quarters. You'll find the stone on the table.
7. player.moveto 0007FB3A or If you purchase Proudspire Manor in Solitude for 25,000 gold after gaining the Jarl's trust, you'll find a stone in the master bedroom.
8. player.moveto 0007F926 or In the Blue Palace in Solitudue check in the Jarl Elisif's quarters. You'll find the stone on one of his shelves.
9. player.moveto 0007FB4A or In Yngvild, a cave north of Winterhold and east of Dawnstar, check behind the throne to find a chamber that is hiding the stone.
10. player.moveto 0007F908 or In the College of Winterhold during the Under Saarthal quest search the shelves of the Arch-Mage’s Quarters to find a stone.
11. player.moveto 0007FB63 or In Hob’s Fall Cave, a cave in the area between Dawnstar and Winterhold, you'll find the stone near the necromancer's sleeping area by the alchemy lab.
12. player.moveto 0007F925 or In the Treasury House in Markarth find the stone next to bed in the master bedroom.
13. player.moveto 0007F909 or In Understone Keep in Markarth, look for a locked door to a side room of the Dwemer Museum. You'll find the stone in the room on a table.
14. player.moveto 0007FB4F or Southwest of Markarth, you'll find Dead Crone Rock. In front of the Word Wall at the top there will be an altar, you'll find the stone on the altar.
15. player.moveto 0007F901 or Inside the Dark Brotherhood Sanctuary, check in Astrid’s room. You'll find the stone on a dresser.
16. player.moveto 0007FB54 or In Thalmor’s Embassy, while on (or after you've completed) the quest “Diplomatic Immunity” for Delphin in Riverwood, check in Elenwen’s Solar. You'll find the stone in a bedroom.
17. player.moveto 0007F95D or In Dragonsearch in Whiterun, check the Jarl’s bedroom to find the stone.
18. player.moveto 0007FB58 or East-northeast of Whiterun you'll find a dungeon called Fellglow Keep. You'll find the stone on the counter of the workroom at the top of the front foyer.
19. player.moveto 0007FB64 or Northeast of Rorikstead and southeast of Marthal you’ll find a dungeon called Rannveig’s Fast. You'll find the stone on a table near the prison area.
20. player.moveto 0007FB5D (if you use player.moveto this spot then do not kill that witch! it will spoil a quest line) or In Ansilvund a tomb in Eastmarch, you'll find a stone in the burial chambers near where you encounter Fjori's ghost.
21. player.moveto 0007FB55 or In Mistveil Keep in Riften find the stone in the Jarl's Quarters.
22. player.moveto 0007Fb56 or East of Riften in the Black Briar Lodge you'll find the stone upstairs in the master bedroom. Note: Black Briar Lodge is different than Blackbriar Manor, so don't confuse the two. 
23. player.moveto 0007FB45 or Northeast of Falkreath  you'll find a farm called Pinewatch. Inside the farmhouse, you'll find a secret entrance to the Bandit Sanctuary. Go there and make your way towards a room with empty draugr tombs. Once there you'll find a locked door directly to your right. Use a lockpick on the door and you'll find the stone on the top shelf of the a bookcase.
24. player.moveto 0007FB51 or South of Gjukar’s Monument and north of Moss Mother Cavern, in Falkreath, you'll find Sunderstone Gorge. Inside, stone on an altar in front of a Word Wall.

Ended up with 23 of the 24 stones? Yeah Yeah we know, Vex likes to keep the stone for himself
The PC version of the game has a nice fix!

• set TGCrownGemsFound to 24
• set TGCrownGemsTotal to 24
• setstage TGCrown 30

If you gather all 24 stones before getting Vex to identify them it won't advance to the stage where you need to turn them back into her and your journal will still say to recover the gems (24/24). On the PC type the following 2 commands for a workaround.

• setobjectivecompleted TGCrown 20 1
• setstage TGCrown 30

player.moveto 00084BEA Once you've found all 24 Stones of Barenziah, Vex from the Thieves Guild will ask you to recover the Crown of Barenziah from Tovald's Cave. According to the Vex, once you recover the crown, which is a paragon for the Thieves Guild, she'll be able to restore it to its full strength and reward you with the Prowler's Profit.

Bron: Skyrim Stones of Barenziah Locations: How To Find All 24 Stones In The Elder Scrolls 5