The problem you have is that the quality of life is in the exactly opposite of quality of education/job prospect.
Olin isn’t on par with UNC or Vandy. I would eliminate this choice.
Vandy: Nashville is a medium size US city, but it lacks diversity. The selection of Chinese food is very limited. I would say only 1 or 2 authentic Chinese restaurants. I don’t think you would be comfortable in the bars or nightclubs here (mostly catering to Caucasians of the country variety). The downtown area is pretty safe.
UNC: CH is much smaller than Nashville, but it has decent amount of activities. The selection of Chinese food is limited, but surprisingly, it is better than Nashville. You are pretty safe in the Franklin road area. The bars and “nightclubs” are catered to people much younger than typical MBA students.