You would like to work in a different city to be closer to your family. Write a letter to your employer to request a transfer to another office. In the letter:
Explain why you would like to move.
Request that your employer places you in a specific city.
Request that it be completed by a certain date.
Dear Sir or Madam,
I am writing this letter to request a change in my work location. I hope you will consider my request.
Let me explain you in more detail. My current location, Banglore, is away from my hometown Ahmedabad where my family resides. As we have inaugurated office in Mumbai last year, it would be great if I am transferred there because it hardly takes few hours to reach my family. Additionally, it will help me to work efficiently because most of my team members are operating from Mumbai only.
Moreover, I have been working with the organization for a decade and I trust you will be considerate of this request. My current rent agreement in Banglore is completing by next month, so it would be a good gesture if you could consider this request prior to the 15th of June which will allow me a smooth transition. Please let me know if you have any concerns.
Looking forward to hearing from you.