Terrance Robinson correctly guessed that Auckland Unitarian Church is the farthest south of any UUA-affiliated church. And it is indeed really, really far south when compared with the rest of the UUA’s member congregations. However, it is not the most southern of all Unitarian groups. That distinction belongs to Unitarians of Christchurch, who are midway down New Zealand’s South Island. The Auckland Unitarians are in fact the most northern of the New Zealand churches. Terrance also guessed Christchurch–not sure if he was trying to answer both questions or just giving two answers for the first one.
Alternately, the bonus question prize could go to Centro Paz y Armonia (Peace and Harmony Center) in Ushuaia, Argentina, one of the most southern inhabited places on the planet. The Center has ties to international Unitarianism but is not necessarily explicitly Unitarian in orientation.
No word yet on when a Unitarians of Antarctica congregation will be officially organized.