It's true that you can easily spend $100 on brunch or $20 on a cocktail in New York, and most museums will cost at least $20 to get in the door. Even movie tickets tend to be pricier in New York City when compared with pretty much anywhere else.
Then, of course, there's rent — only San Francisco has higher average rent in the US, and New Yorkers can easily expect to pay thousands of dollars to live in a tiny apartment with three roommates. Even chain restaurants, gyms, and supermarkets like Whole Foods are pricier in New York City when compared to other cities.
But at the same time, it's possible to get by in New York without completely breaking the bank. There are always free events going on, from concerts to free museum nights to movies in the park.
New York is also one of the best cities for truly amazing cheap eats. For starters, there are countless dollar-slice pizza joints all across the city, Halal Guys carts for gyros, Yu Kitchen for killer dumplings and wontons, and if you really want a hot dog, skip the stand and beeline for the Papaya King — and get a juice while you're there.
If you're responsible and do your research, New York City doesn't have to be cost-prohibitively expensive.