The Bedlam Job

The Bedlam Job are quests given to you by Delvin Mallory in the Ragged Flagon as extra work for the Thieves Guild. The purpose of a bedlam job is to steal a bunch of goods from towns around Skyrim.
 * 1) Steal 500 gold in goods from Riften.
 * 2) Steal 500 gold in goods from Markarth.
 * 3) Steal 500 gold in goods from Whiterun.
 * 4) Steal 500 gold in goods from Windhelm.
 * 5) Steal 500 gold in goods from Solitude.

You may need to steal 500 gold worth of items from the respective hold's keep. It is more of a Robin Hood thing in which you steal from the rich, in this case the Jarl of the hold, and give to yourself.

Confirmed you do not need to steal from the city's Keep, anywhere around town will usually work. But not always. (ex. Riften)