Which direction should the headboard face?
There are 2 opinions as to the proper position of a bed. According to the Talmud it seems it should be placed between North and South. According to kabbala it should be placed between East and West. Both are valid opinions, one who generally follows Kabbalistic teachings should do so here as well.
Aside from the above, there is a custom not to sleep with one’s feet directly facing the door.
See Shulchan Aruch 3:6, Mishna Berura ibid. 11, Aruch Hashulchan ibid. 13, 240:17, Kaf Hachaim 3:16, Shu”t Or Ltzion 2:1, Shu”t Vayashev Hayam 1:1.
With regards to facing the door see here.