'hit' implies movement from a location, suggesting that the person is coming from somewhere that's not 'here'.
Fveldig's explanation is accurate.
The words hit og dit (here and there) are comparable to "hither and thither," as in, "In my free time, I like to travel hither and thither."
With the word, hit, the sentence means, "Do you come to [this place] often?" Coming to [this place] implies movement.
Thank goodness english dropped those words lol.
Thither just sounds so odd. Sounds like something a snake would say.
They are quite useful and precise, in my opinion, but people dropped them for convenience and just rely on context. :)