Nicely done! However, I do think that you should keep as much focus on the school as possible, so mention the ethnic diversity of the campus, not just the city. Other than that, I don't see anything else worth correcting.
Not only that, Miami is also ethnically diverse so waking up to anything less that just wouldn't work.--phrasing is repetitive, and ethnic diversity could be incoorporated elsewhere.
I cut out that sentence entirely. How does this sound?
When you get past the bright lights and fast pace, New York is a dynamic melting pot full of inspiration. It's no wonder millions of people go there to fulfill their aspirations. Coming from Miami, I wouldn't be able to settle for anything less than a big city atmosphere, and they don't call New York "The Big Apple" for nothing. I've been exposed to multiple walks of life. I've learned so much from each and every person I've met. I want to continue my pursuit in learning from unique people not only in the city but in NYU's diverse campus as well.
just make sure you really play up academic rep if you go with that
NYU Steinhardt's media, culture, and communications program provides the rigorous coursework needed in challenging any aspiring student and stimulating their growth. As a persevering student, this exceptional program will push me to perform beyond my greatest capabilities.
Is this any better?
P.S. Thank you so much!