Juneau, Alaska
The Alaska State Capitol in downtown Juneau was originally built as the Federal and Territorial Building in 1931.  Prior to statehood, it housed federal government offices, the federal courthouse and a post office.  It also housed the territorial legislature and many other territorial offices, including that of the governor.  Today, it is still the home of the state legislature and the offices of the governor and lieutenant governor.  Other executive branch offices have largely moved elsewhere, in Juneau or elsewhere in the state, in the ongoing battle between branches for space in the building, as well as the decades-long capital move issue.  Recent discussion has been focused between relocating the seat of state government outside of Juneau and building a new capitol building in Juneau.  Neither position has advanced very far.  The Alaska Committee, a local community advocacy group, has led efforts to thus far keep the capital in Juneau.