Washington is the seat of government of the US.

华盛顿是美国政府所在地。

Gunfire broke out early this morning around the seat of government in Lagos.

今天清晨在拉各斯政府基地周围爆发了枪战。

Exactly. Zicheng of Jiaxing was the local government seat in many dynasties.

没错。嘉兴的子城是嘉兴历代府衙的所在地。