Is there a realistic chance to get a Sysadmin job in NY area as foreigner?

I hope my fellow Redditors can encourage me with their experiences. :)

I am from Hungary (heart of Europe). I am a 27-year-old and I have almost 5 years of experience managing big Windows Server environments.

I had a few weeks long holiday in the US 3 years ago, and I will spend my summer holiday in NY area this year as well.

Recently I started thinking about getting a new job somewhere else, because in my current position there isn't enough challenge, and I'm just wasting my skills and my enthusiasm there. So I started to dream and dream big: Maybe I should apply for a job in the United States.

While I was researching this topic, I have realized that unfortunately it's really hard to get a Visa and to work in the US legally, and it seems there isn't too much chance for this.

What are your experiences? Could you get a job in the US? Does the average American accept and value a skilled but foreign colleagues? Do you have a career opportunites?