Click here for more info on the East Empire Blessings and how convincing the Jarls works.
While the camp exists immediately for Whiterun, in order to get access to Location Claiming in the Whiterun area, the Jarl must be convinced to give his blessing still.
The following options are available for both Balgruuf and Vignar Gray-Mane:
In addition, if Balgruuf is the Jarl, a Gift option (see below for details) and Perk option (Shield Charge) are available.
If Vignar is the Jarl, Gossip and Coerce options are available (see below for details)
The "Family Amulet of Talos" unlocks the Gift option for Balgruuf. The clue that this exists is a note called "Note to Jarl Balgruuf" that can be found on the war table in the upstairs of Dragonsreach.

The amulet can be found in Shimmermist Cave in a chest near a pile of bandit corpses.

A note called "Note about Jarl Vignar" unlocks the Gossip option, and can be found on the bar in the Bannered Mare.

A note called "Gray-Mane Documents" unlocks the Coerce option, and can be found on the nightstand to the right of the bed in the main bedroom on the upper floor of House Gray-Mane.
