Stones of Barenziah

Finding one of these unlocks new miscellaneous quest, Bring the Unusual Gem to an appraiser, in which one of these stones must be identified by one of several appraisers; two of which are Maul in Riften and Vex, part of The Thieves' Guild, also in Riften.

Upon getting it appraised, the player learns that 24 exist in total and that they are only valuable as a complete set. Most, around 20, can actually be found via systematic exploration without requiring to join any faction or playing the main quests. A few of them can only be found as part of extra jobs for The Thieves' Guild. The reward for collecting all of the stones and then replacing them in the Crown of Barenziah, thus transforming it into Barenziah's Crown, is a perk called Prowler's Profit.

Locations

 * 1) Ansilvund, in Eastmarch, contains a stone near where you encounter Fjori inside the burial chambers.
 * 2) Black-Briar Lodge, outside Riften, the master bedroom.
 * 3) College of Winterhold on the shelves of the Arch-Mage's Quarters.
 * 4) Dark Brotherhood Sanctuary, look in Astrid's room for the stone. This stone can only be found while completing the “With Friends Like These...” or “Destroy the Dark Brotherhood!” quests.
 * 5) Dead Crone Rock, south-west of Markarth. The stone can be found on an altar near a Word Wall at the top.
 * 6) Fellglow Keep, can be found east-north-east of Whiterun. Look on the counters of the workroom to find this stone.
 * 7) Hob's Fall Cave. The stone is inside the Necromancer's sleeping area.
 * 8) Markarth, the Treasury House, search the master bedroom to find the stone.
 * 9) Markarth, in the Dwemer Museum. The stone will be inside, on a table behind a locked door.
 * 10) Pinewatch, a farm north-east 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.
 * 11) Rannveig's Fast, north-east of Rorikstead and south-east of Morthal. Look for a prison area, and search the table with the Alchemy Lab for the stone.
 * 12) Riften, Mistveil Keep, the Jarl's Quarters.
 * 13) Solitude, just outside town, on The Dainty Sload, a boat. Look in the Captain's Quarters, on the table.
 * 14) Solitude, in Proudspire Manor. You'll find the stone in the master bedroom.
 * 15) Solitude, in the Blue Palace. Look in the Jarl's quarters, on one of her shelves.
 * 16) Stony Creek Cave, can be found north of Ansilvund, south-east of Windhelm. Look in the area where you encounter the Bandit Wizard.
 * 17) 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.
 * 18) Thalmor Embassy, look in Elenwen's Solar while completing the "Diplomatic Immunity" quest for Delphine in Riverwood. If the stone is not in the Solar, it will likely be in the Reeking Cave on the way out.
 * 19) Whiterun, in Dragonsreach, explore the Jarl's bedroom to find a stone.
 * 20) Whiterun, Kodlak's room in Jorrvaskr.
 * 21) Whiterun, Hall of the Dead, check the wall crypts to find another stone.
 * 22) Windhelm, House of Clan Shatter-Shield, simply search the first upstairs bedroom to your left to find the stone.
 * 23) Windhelm, Palace of the Kings, look on the table in Wuunferth the Unliving's Quarters.
 * 24) Yngvild, a cave north of Winterhold and east of Dawnstar. Search behind the throne to find a chamber containing the stone.

Bugs

 * Alas the Prowler's Profit may not actually be shown under the active effects in the menu.