By RCA Building you mean Rockefeller Center right? You really need to ask yourself what reasonably close to Rockefeller Center is. Do you mean 10 minute subway ride or 30 minute subway ride? Close in distance to Rockefeller Center would put you in Midtown somewhere or the Upper West Side, both of which are pretty pricey. If you’re willing to go for a bit longer commute, like 20-30 minutes, you could live in Harlem or Hamilton Heights, which is the historic district within Harlem. There are other options too, like Astoria in Queens or various neighborhoods in Brooklyn or even New Jersey, especially Jersey City.
My best advice is to come visit with your parents for a weekend. The city isn’t the big scary place it used to be, aka the 70s and 80s. That way you can see the neighborhoods and your parents will be a bit more comfortable with you moving here.
You should also check out Craigslist to get an idea of the prices for renting an apartment. If you start now, you might get over the sticker shock and you’ll be able to limit your search when you are ready to move.
My other advice is it’s much easier to find a job in the city when you’re actually here. Trust me on this one, I know from experience. This is totally shallow but employers look for the NYC addresses. It might be worthwhile for you to find a job at a store or something to pay rent and give you time to find your dream job. Or, if you have freelance-able skills, start talking to your professors and alumni to make conncections.
This is kind of long but I hope it helps. Moving to New York is crazy, exciting, and scary all at the same time. If you have any other questions just let me know.