There are two standard expressions I know of, that use these words. Both are rather old-fashioned, but I wouldn't yet describe then as archaic. Examples:
The crowd ran hither and thither in confusion. The crowd ran back and forth, they ran aimlessly.
Yeah, "hither" = "to this place", "thither" means "to that place", and "whither" means "to what place?". There is a whole little set of words that begin in h-/th-/wh- and all follow the same pattern. Cf.
As has already been said, there's a wh/th/h thing going on. What made me notice it was the correlative system in Esperanto, so I'll call them correlatives HENCE forth (from this place forwards) if I need to.