These Stones fo Barenziah really are scattered all over the place, but are mainly concentrated in places you need to visit for various semi-major quests. Quests like the Dark Brotherhood, Theives Guild, College of Winterhold, Stormcloaks/Legion, etc. often bring you within reach of these objects. However, for your convenience, I have put together a list of exactly where each of them is. I'll be updating the details as I go back through the game for a second time.
| 
Location | 
Notes | 
| 
Whiterun | 
Halls of the Dead Catacombs (in the
  first room, go down the left stairs and it will be to your left) | 
| 
Whiterun | 
Dragonsreach (Jarl's room) | 
| 
Dark Brotherhood Sanctuary | 
Astrid's room. Still accessible after
  the Death Incarnate quest. | 
| 
Whiterun | 
Jorrvaskr (Kodlak's room) | 
| 
Solitude | 
Blue Palace (Jarl's room) | 
| 
Thalmor Embassy | 
Elenwen's Solar on the second floor. | 
| 
College of Winterhold | 
Arch-Mage's Quarters | 
| 
Black-Briar Lodge | 
East of Riften (second floor bedroom,
  next to bed) | 
| 
Riften | 
Mistveil Keep (Jarl's room) | 
| 
Markarth | 
The Treasury House (end table in
  Thonar's bedroom, which is the left from the front door) | 
| 
Windhelm | 
Palace of the Kings Upstairs (Wuunferth's
  Room) | 
| 
Markarth | 
Understone Keep - Dwemer Museum
  (on a table in the first room to the left) | 
| 
Fellglow Keep | 
Northeast of Whiterun (straight up
  the stairs and to the right) | 
| 
Stony Creek Cave | 
Just North of the Ansilvund
  Burial Chambers (last room on the table) | 
| 
Windhelm | 
House of Clan Shatter-Shield | 
| 
Solitude | 
Proudspire Manor (must be
  purchased for 25 000 gold) | 
| 
Pinewatch | 
In a house west of Helgen there is a
  secret hideout accessible from the basement. | 
| 
Yngvild | 
The island northeast
  of Dawnstar (bedroom behind the throne in Yngvild Throne room) | 
| 
Dainty Sload | 
Ship along the coast southwest of the
  Solitude Lighthouse (last room on the table) | 
| 
Sunderstone Gorge | 
On the table with two bodies in front
  of the Dragon Word Wall. | 
| 
Dead Crone Rock | 
On the stone table opposite dragon
  word wall. | 
| 
Ansilvund Burial Chambers | 
Northeast of Shor's
  Stone and due north of Riften. | 
| 
Rannveig's Fast | 
After falling down the trapdoor in
  front of the chest and Dragon Word Wall) | 
| 
Hob's Fall Cave | 
On the northern coast, directly
  between Dawnstar and Winterhold. Near the alchemy set. | 
If you have any trouble finding any of these Stone of Barenziah locations, please let me know. As I said, I'll be updating as I go through the game again, so if I need to revisit any particular part sooner rather than later, I can do that.

 
 
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