What advantages did romes geography provide for the empire

 Well if you are only referring to the city its self it is quite simple. 
It is settled on the Tiber River which is one of the major rivers of Italy and that region. So Rome benefited from all the advantages from of being on a river travel, drinking water and access to the Mediterranean for trade. Rome as surrounded by very fertile land from which it could grow lots of crops. once Rome took over Italy the two main mountain ranges acted as protection, the Alps to the North and the Apennine on the spine of Italy to the East. Finally, due to Italy jetting out into the Mediterranean sea, Rome had the perfect launching point to control it both in trade and militarily.