Yes! This person was living in East Village, which is probably the most happening/hip neighborhood in Manhattan. Tons of bars, restaurants, theaters, other young people. Neighborhoods in upper Manhattan, Queens, Brooklyn, and Jersey City have easy access to the city (30-45 min train rides) and cost less.
I don't think it makes sense to live in New York unless there is something you can only get here. There's only one MoMA, one City Ballet, one Film Forum. (Not to mention the business and professional opportunities - the city is a business city first and foremost.)