City states. Tribalism would result in power being held by the largest most well armed tribes.
Pretty simple walled urban areas serving as the main centers of governance, and stockpiles, a walled industrial area, a walled residential area, a final militarized ring to protect it all and a territory that would be claimed and used for natural resources and further farming. There will be weapons on the earth for generations after the fall. You can also expect that rebuilding weapons will be one of the first industries to spring back.
Elder Council. With a representative of each group from the guilds, merchants, farmers, military, and any other relevant group. Major decisions would be voted upon by the Elder Council. Each member would receive one vote. There would always have to be an odd number of Elders.