The Bedlam Job

Background
It is a repeatable quest given by Delvin Mallory in the Ragged Flagon as extra work for the Thieves Guild. The object of a bedlam job is to steal 500 worth of goods from one of the following Holds:
 * Markarth (the Reach)
 * Raven Rock (Solstheim)
 * Riften (the Rift)
 * Solitude (Haafingar)
 * Whiterun (Whiterun Hold)
 * Windhelm (Eastmarch)

If enough of these quests are completed, special City Influence quests will be unlocked, which will expand the Thieves Guild (and unlock new fences).

Markarth

 * Endon's House. In the bedroom on top of a dresser is a silver necklace worth nearly 600.
 * The blacksmith area inside Endon's house has valuable steel weapons and silver ingots.
 * Also inside Endon's house there are 2 locked display cases (Adept) containing some valuable rings and necklaces.
 * The Treasury House has six silver ingots, a safe with over 200, along with at least one gem and a high value enchanted weapon, easily totaling over 500 . It also has a Stone of Barenziah in the bedroom, right next to the bed.
 * The Dwemer Museum has a Stone of Barenziah and a large assortment of goods with only two guards. (Almost all of these items are locked in display cases which will increase lockpicking as well.)
 * If "The Forsworn Conspiracy" has progressed past the point where Nepos the Nose is dead, Nepos' House has enough loot that respawns to complete the job, with no one on guard.

Raven Rock

 * With the addition of, Bedlam jobs are available in Raven Rock. There is an East Empire Company Strongbox in the Bulwark with more than enough loot to complete the job.

Riften

 * In the Black-Briar Meadery, behind the counter, to the left there is a leveled sword worth a good part of the needed.
 * Madesi's stall in the center of town has extremely valuable jewelry in the display case.
 * Grelka's stall, to the right of Madesi's contains several valuable pieces of enchanted armor, along with some valuable jewels in her strongbox.
 * Brand-Shei also has several valuable gems in his stall's strongbox.
 * There is a Stone of Barenziah in the Jarl's quarters in Mistveil Keep. Taking this completes the quest.
 * Unlock Grelka's stand. Inside the are several pieces of enchanted armor, taking just one can complete the quest.
 * If unlocked, the alchemy store in the Ragged Flagon will have quite a few valuable potions, some of which are 500 or more.
 * If unlocked, the archery shop in the Ragged Flagon has an enchanted bow worth much more than 500.
 * The Riften warehouse has skooma and Moon Sugar.

Solitude

 * Bryling's house; she has several valuable potions and is very rarely home.
 * The righthand room of the top floor of The Winking Skeever has potions worth the required amount of gold.
 * The Thalmor Headquarters in Castle Dour has no shortage of valuable potions, has no lock on the door, and has no one standing guard.

Whiterun

 * In Dragonsreach, in Farengar's quarters, there are several valuable soul gems and potions that are easy to steal and quickly add up to over 500.
 * In Jorrvaskr, in Kodlak's room. One of the Stones of Barenziah is on the cupboard.
 * In the Dragonsreach Jarl's Quarters, a Stone of Barenziah is on the end table to the right of the Jarl's bed.
 * In the Dragonsreach Jarl's Quarters, there's a bunch of display cases with valuable weapons and armor.

Windhelm

 * In Wuunferth's room, on the upper floor of Palace of the Kings in Windhelm, there are potions and scrolls worth well over the required 500 . There is also a Stone of Barenziah in the room.
 * Calixto's House of Curiosities. On a shelf to the left will be two scrolls, each worth 500, along with of many other items. Not only do these items respawn, but if "Blood on the Ice" has been completed, nobody will be there.
 * There is a warehouse on the waterfront that has no guards. It has a potion to the right upon entry that will fulfill the quest.

Trivia

 * While the quest points to the city named, the items can be stolen from anywhere in that city's hold.
 * Items taken by pickpocketing do not seem to count.
 * Being arrested during the job will cause the quest to fail.
 * Being caught stealing an item will prevent it from counting towards the total sum stolen, even if the Dragonborn is not arrested.
 * Killing someone will not fail the quest, so long as it is undetected.
 * If this job takes place in the same town as one of Vex's jobs, her items count towards the total, meaning both jobs can be completed at the same time (does not always work).
 * Returning to a location where an item was placed for one of Vex's Shill jobs and taking that item counts towards the amount needed.
 * If an item is stolen, dropping it and then picking it back up it may count as a new theft towards the total. If a reasonably valuable item is found, it may be possible to steal it a few times rather than searching for other items.
 * Taking one of the Stones of Barenziah will fulfill this requirement of 500 despite its lower listed value and it being taken rather than stolen.
 * Alchemy shops have valuable goods (void/frost/fire salts, potions, etc.).
 * The Jarl's room or castle has jewels to steal.
 * Jewelry stalls in cities usually have items that have a high value, it may be possible to complete a Bedlam Job by stealing only one item.
 * Winning a brawl with someone counts towards the total.

Bugs

 * The Raven Rock bedlam job will not flag as complete even though goods worth over 500 are stolen.
 * Solution: With console command, the goal will be reached and the quest journal will be updated to return to Delvin to finish the quest.
 * Another solution is to return to Delvin and quit the job. After doing that, ask for it again. If you get Raven Rock, just quit the job.
 * Stealing a single item worth exactly 500  (e.g. a flawless sapphire), appears to not fulfill the requirement. Stealing items above this total appears to trigger completion, so 501 may be the actual threshold.

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