Both the sons and daughters of Zeus reside in Cabin One of Camp Half Blood. Originally, there was only Jason Grace and Thalia Grace, but the oath for the Big Three not to have children was dissipated after the War. Due to this, the cabin has now acquired several more campers.
Zeus is the king of gods, so it is natural for his children to be leaders or excel at showing leadership. As he is also the god of the sky, many of his children can control weather or fly.