I decided to explore the West Corridor first leading me to the Senate room.
They also said that it is standard procedure to have a governor's portrait commissioned after the term is over. So our current governor, Mark Dayton, will have his portrait done when he is out of office. That explains why I couldn't find it.
Continuing on then through the building brings one to the Minnesota Supreme Court. This room is opened for tours and otherwise the greeting is another locked gate.
The last area to explore on this floor is the House of Representatives. For anyone from the public, the best way to view this room is from the gallery on the 3rd floor, as the 2nd floor perspective is through another locked gate.