If you want to ask where someone is living, you'd usually ask "Where do you live". You can say "Where are you living" if they're living somewhere temporarily and will go soon (ex. If they're an exchange student). If their stay is much more brief (ex. they're on holidays), you'd say "Where are you staying". If you want to ask where someone is from, you'd say "Where are you from?" or "Where do you come from?", to which the answer could be a city, country, continent etc. If you only want to ask about the city you could say "Which city are you from?" or "What city do you come from?", although I'd probably say something like "Where exactly are you from?", in which case they'd give you details (probably both the country and the city).

maybe you can ask "What is your native city?" and "Where are you living" - question where is someone live currently :)

Both are correct grammatically. "Where are you living?" suggests the arrangement is not permanent.