The manga is quite different from the anime. No TV Station. Her domain isn't even on Earth, rather it lies in the center of the galaxy at Zero Star of Sagittarius. Her "home" is a castle which almost looks like a large cathedral. Very tall and elegantly decorated. We don't get to see much of what the inside looks like, except for small look at Galaxia's bed. No throne is seen, but seeing that she considers herself above everyone else, she probably has one. She has a large globe that she uses to see earth and the Galaxy Cauldron.
In order to reach this great castle, one must cross the two Rivers: River of Memory and River of Oblivion. Just behind the rivers is the Graveyard, guarded by the "Soul Hunter." If you make it through there, the two Star Gardeners are what's left in the path.
Of course, even making it through there still doesn't mean you'll be able to find the castle itself for Galaxia is able to make it appear and disappear at will.