"My hometown is a good place for living in."
"My hometown is a good place to live".
They are both grammatically correct and it could be argued that the meaning is the same.
For me there is a difference.
"My hometown is a good place for living in." This means that my hometown has good facilities: cinemas, music venues, sports arenas, restaurants etc. The town supports the everyday activities of living.
"My hometown is a good place to live". This could mean the same but to me it means that it is good because it is in a good location or is situated somewhere important. For example:
"My hometown is a good place to live because it is near the university that I want to attend. I'll be able to visit my parents and friends regularly".