Columbia, paired with New York City, is abundant with opportunities. Its breathtaking campus is small enough to not feel lost in the crowd, yet large enough to meet unique people and explore NYC, from Grimaldi's Pizzeria to the Staten Island boat graveyard. Most importantly, it is easy to find balance in (deleted one's, a bit awkward in terms of wording) life.
Try giving an example of finding balance. You did mention the crowd size/diversity for meeting unique people, but I think that's common for a lot of cities/places. Find something very unique to NYC and Columbia. I would try the contrasting/different cultures and options in the city, ranging from food (dollar pizza near Union Square to higher end restaurants on the Upper East Side) to unique internships and city-wide opportunities.
Lastly , Columbia's focus on multi-disciplinary learning, especially through Core, is fundamental to personal development and provides the opportunity for me to apply my leadership skills and innovative thinking. In order to balance the stressful academics, exciting traditions (such as the 40s on 40s and the Primal Scream) are always available to let loose. Columbia is the one place where I can obtain a prestigious education in the most exciting city in the world has to offer.
Overall, it's very well written. I've never been able to write "Why (College)" essays very well, but I think you've nailed it here. Are there any other specific requirements/prompts?
EDIT: Wait, your title says "Why NYU" but you're talking about Columbia. I see you also have another columbia prompt, did you get the two mixed up?