In a more colloquial and shorter sense, you can just ask: "Saan magandang magpagupit dito?" Where 'lugar' is common sense /given that you asked "saan" 어디. It's more of 어디 than 무슨. 'pinakamaganda'보다 'maganda' 더 좋다 since places would vary and when you ask where's 'magandang pagupitan', people will already say the best place they know. 'pagupitan'보다 'magpagupit' 도 좋다 because it is being assumed that when you look for a 'pagupitan', you will be availing their service and you're 'magpapagupit'.

saang lugar dito ang pinaka-maganda/maayos para makapagpagupit? or saang lugar pinaka-maganda/maayos na pagupitan dito? ^_^ saan = where (saang is just for the ease of pronunciation) best=pinaka (maganda and maayos both are both positive descriptions but have different meaning and i just used it here in the sentence to emphasize what kind of goodness you are saying ^_^) place=lugar dito=here para=to, so that makapagpagupit=to be able to have a haircut (while 'pagupitan' is the place where you had your haircut) hope you understand ^______^ 화이팅