depends- if you are talking about right now, then "where are you staying?", if talking about what you do normally, "where do you stay?" e.g. "where are you staying tonight?" (now) but "where do you stay when you visit Sydney?" (always)

here's my explanation where do you stay? = permanent address or long term stay where are you staying? = short term stay for example, if you have an english speaking friends visiting china, you should ask: "where are you staying?" then he can reply "I am staying at Gangbang Hotel."

This is a question about tenses..."where are you staying" implies, where are you currently, in the present. Where as "where do you stay" implies some kind of future tense i.e. when you go to ...... where do you stay? Or when you come to ........ where do you usually stay?

It is a question based on tense-present ,normally when we ask a person where he/she is staying for the present location we ask "where are you staying?'and in a converastion when we enquire a persons whereabout we ask "where do you stay?