In The Elder Scrolls V: Skyrim for the PC, PS3, and Xbox 360, Proudspire Manor is the house you can purchase in Solitude once you gain enough favor there. Proudspire Manor is also the largest, must luxurious house in the game costing a whopping 25,000 gold to purchase, and another 11,000 gold to fully upgrade.
To buy Proudspire Manor, you need to do quests for the Jarl in Solitude, up to and including Elisif’s Tribute. Falk Firebeard will give you the majority of the quests, most of which include some rituals that are going on in Wolfskull Cave.
Once you complete Elisif’s Tribute, the Jarl will allow you to purchase Proudspire Manor.