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'.