"or is he dead by now and down in Hades’ Halls?"
Hades was the god of death and ruler of the Underworld
, so by ‘Hades’ Halls’, Penelope means the Underworld. In Homer’s epics, the Underworld seems to be portrayed as a dreary place and the afterlife a depressing existence. In most accounts, it is split into three main sections: Tartarus, where terrible sinners are punished, the Elysian Fields, where the heroic and the virtuous go, and the Meadows of Asphodel, where the average person would reside. In Homer’s account, the Elysian Fields appear to have been reserved for only very special people, such as those related to Zeus.