The Romans did not have buildings designated
as headquarters. If you are referring to the army, during a
campaign, the winter quarters/camp (castra hiberna) acted as
headquarters. Fighting occurred during the summer and when the army
moved around it set up summer camps (castra aestiva or aestivalia)
which were temporary and where the soldiers slept in tents (sub
tentoriis). The castra hiberna had barracks which were originally
made of wood and later of stone and were more like forts. When
troops became permanently stationed in a region they had castra
stativa, standing camps. These would act as headquarters.