When you say New York City, do you mean Manhattan, or all the boroughs. You may mean Manhattan. That's usually what most people who aren't from the area think, because it's what they see on TV and in the media. In the New York area, people ackowledge all the 5 boroughs as NYC. Generally, excluding Staten Island, public transportation is very good throughout the entire city. You save a lot of money not paying for parking, gas, car insurance and car loans. That right there may alone compensate for the extra few hundred a month you may spend on rent compared to elsewhere in the country. The more expensive lifestyle you want though, the more you'll pay. That all depends on your taste though. If you want a decent one bedroom apartment, with a decent amount of space, in Brooklyn or Queens, it'll be around $1,100 to $1,200 per month. In Manhattan, it's nearly double. When talking about Manhattan though, half the population lives north of 96th street, while the other half lives below 96th street. Very few people below 96th street are native New Yorker's. It's one of the most touristy places in the world. They're there 24/7. You can't even decipher who's a commuter, who's a resident and who's a tourist. It's nearly impossible. You'd pay about $2,500-$3,000 a month there. On the Upper West side, it's probably more around $2,000 to $2,250, but less people work there, so you have more space. Once you started going past around 110th street, it's not really Manhattan anymore. Yes, it technically is, but it doesn't have the same vibe. It relates more the other boroughs, especially the Bronx, which it's in close proximity too. It'll cost similarly to Brooklyn and Queens there. Like Brooklyn and Queens, ''yuppies'' or American transplants, have migrated into these neighborhoods, but they don't dominate them. There's a lot of ''traditional'' foreigners living there, mainly Latin American's (ex. Dominicans, Mexicans, Colombians), but probably within the next decade, it'll be another twenty-somethings hipster paraside like Williamsburg. The reason why rent in New York is expensive is because of it's demand. What makes Manhattan more expensive than the other boroughs though are smaller things, like food. There's few supermarkets. Most people don't have cars, so they can't drive out to Queens, or somewhere else to get their food. So, most people eat out, or shop from closeby delis, which are expensive. Either that, or you could Costco it, and eat by bulk, but most people in Manhattan think they're too ''high-end'' to do that.
You ask about children? Well, in Manhattan, a lot of people don't have children simply because it's that expensive. That's not just there, but it's popular in lots of major cities worldwide, like Tokyo, Paris, Rome and other cities. The fertility rate is generally lower amongst wealthier and more educated American's. Most families probably only have one kid. They usually do put their kid's in private school, but if it's only one child, and you're not feeding and clothing two kid's, like the average American family, the extra money spent on education really isn't that big a deal. There's also a large homosexual population that obviously doesn't have children.
A lot of people who live in Manhattan though are what you may call ''semi-permanent.'' Young people in their mid-to-late twenties either graduate from colleges here, or move here, start careers, and by the point they're in their late 30's/early 40's, they realize they have a choice to make. Most people get married by this point and want to start a family, even if a small one. Choice one is to stay in Manhattan, with the burdening expensive. Some people choose this, but the majority don't. Choice two is to move to another borough. Some do this too, but most don't. Choice three, probably the most common one, is to go back home, but the problem is your spouse probably isn't from the same place. Choice for is go to your spouses home. Or choice five, possibly do to voluntarily relocating your job, pick a new random area (ex. Florida). This is why you don't see many people in Manhattan doing the traditional move to growing places like Florida or Nevada. It's because barely anyone is from New York and they have close family and attachments in where ever it is they're from. Unfortunately, the same lucrative business job may not exist in like Cleveland, so sometimes tough choices have to be made. Sometimes, these people are so well off, they could practically semi-retire by their early-40's.