What an advertisement says a company requires and what a company really requires are often two different things. If you can demonstrate your capability as a programmer, that’ll be enough - maybe not for every company, but most definitely for someone.
Take a look at the job listings on indeed.com. There’s almost 4,000 of them. Compare this to Denver (~900), Houston (~600), and even San Fransisco (~2,500). The average wage for web developers is about US$90k, which is much higher than average (if I remember correctly, it’s the second highest in the country). So, there are lots of opportunities for web developers. Culturally, it’s also quite diverse. Queens has the most languages spoken in one place than anywhere in the world, so you may find a small community of people from your own country. Who wouldn’t want a little slice of home life when moving to another country?
But hey, you’ve read it here before and you’ll read it again. NYC costs a lot of money. Manhattan rent is trending downwards, but still sky high. NYC also levies an additional income tax on top of your state and federal taxes. Living on campus would definitely be cheaper, but you’re still going to be paying for the privilege of living in the city. There are plenty of places that wouldn’t be as expensive, and some of them would be interesting, but you’re young and starting life. If you think you’d like New York, go to New York. Don’t settle. It’s just money.