In The Elder Scrolls V: Skyrim for the PC, PS3, and Xbox 360, Hjerim is the house you’ll be able to purchase in Windhelm once you gain enough favor with the Jarl there, and costs 12,000 gold.
To purchase Hjerim, you need to do either the Stormcloak line of quests, or the Imperial line of quests. Once you make it to a certain point in either of those factions, you’ll be able to purchase Hjerim.
In order to upgrade the house, you’ll need to do the Blood on the Ice quest given by Wuunferth in the castle in Windhelm.
