Your target schools won't like your undergraduate GPA, but Wharton for one is known for showing preference for GMAT over GPA, so at least for Wharton, you have a better shot. Certainly the perspective you have as an investment banker from Turkey will put a different and more attractive diversity play on your profile vs. all the US based investment bankers, but you will need to elaborate on how this perspective is unique and advantageous vs this large applicant pool with mostly western banking backgrounds. There are a lot of different angles you can use for this, but in the end as long as you are passionate about your post MBA vision and can compellingly convince them that now is the ideal time for you to go back to school, you should get attention.
REgarding your follow up questions:
1) My post-MBA goal is private equity. Will mentioning this in the essays lower my chances? (Since it's very hard to get a PE job after MBA, especially as an international) Should I just say that I want to continue in investment banking? (This is a safer route)
Yes it's nearly impossible to get an "entry level" post MBA job in PE, so I would not mention that as a short term goal.
2) Is this a valid answer to "Why MBA?" question: I want to live in New York for some time.
That would be a better answer to Why Columbia. You can live in New York without an MBA, so I would not use that as a primary reason for Why MBA.
3) Is applying to Columbia ED a logical choice for me? Or do you think I would be competitive at Wharton? (If I apply CBS ED and get admitted, I'll always wonder whether I had a chance at H/W/S)
REgret is a terrible thing. Always apply to your dream schools, that way you never have to wonder....