Hi there,
I can understand it's tough to really get a feel for NYC and its real estate market etc when you haven't lived/worked there, but to a certain degree it is a difficult question to answer except to say it is a huge RE market and extremely active, competitive, and expensive (both residential and commercial real estate). It's also a huge hub for developers and businesses that deal with every aspect of RE. In terms of the cost of real estate itself in NYC, it's known for being one of the pricier places in the US because land is at such a premium with 8 million-ish people in NYC, over 1.5 million living in Manhattan itself which is a fairly small island, and so the city has built upwards for the most part, with some of the tallest buildings and skyscrapers etc in our country. Space is at a premium.
I did live and work in NYC for several years (lived in Brooklyn and worked in Manhattan) and can comment generally on life there but I do not have experience in the RE industry so cannot really comment further on that. I would just point out that Columbia is a great program that has a strong RE focus and will be a great resource for helping you to set up internships, projects with companies, interviews, etc. And the city itself would be a great place to learn more about RE with it's bustling, fast, competitive environment. There also seems to be more interest among MBAs in the RE industry, see
https://www.businessweek.com/articles/20 ... ing-is-hot for example.