If a case has gone through the EEOC complaint process, it will go into the federal district court closest to you. Department of Labor cases can go into federal administrative courts.
Government employee complaints are appealed to the Merit Systems Protection Board, which holds an administrative trial and can go into the state federal court system. Unemployment benefits cases can end up in a local county civil court.
As for the states, each state sets the path that cases go on during an appeal. Some agencies have their own administrative courts and may allow cases to proceed into state civil courts.