Doctor Fate plays his cards very close to his vest in his first year of operation. We don’t get a whole lot more information about him than we started out with: magic guy, cool helmet. We do however learn where he lives:

Doctor Fate’s fourth appearance marks the first appearance of his iconic headquarters, the mysterious ancient tower with no doors that stands outside of Salem, Massachusetts (and it is as always pretty gauche to link Salem to actual magical activity, given all the murders). The tower gets a bit of fun lore (maybe it was built by Vikings!) and features a secret door that is very much not going to stick around. (More Fun Comics 058, 1940)

Just two issues later, in fact, in More Fun Comics 060, the secret door out and walking through walls is in.