Mayor's House is a house in the town Crosswych, Glenumbra. When the Vestige arrives for the first time, the town has been taken over by Red Rook Bandits. After the related quests for Crosswych have been completed, everything goes back to normal.
Tamien Sellan says the Crosswych resistance has gained enough momentum. It's time to deal with the Red Rooks leader, Sternis Gelves himself. The Vestige needs to access the Mayor's House and kill him.