Like others have said, JetBlue, Southwest, or AirTran (though they might have merged with Southwest?) are all good deals for flights.
That being said: Flights in the US are still really expensive.
My mother worked graduate admissions at the local university, which involved a LOT of international students, and she always told me that it's pretty common for a lot of people from Europe or SE Asia just to not really comprehend the sheer magnitude of the US. Like, you get it intellectually, but you don't really GET it. NYC to Vegas is like Lisbon to Kiev. You basically waste an entire day in travel, even without major layovers.
If you're going to be coming to NYC and looking for other places to go (not that I necessarily recommend it -- NYC is an amazing town with TONS of things to discover, both tourist-y and under the radar), your best bets would be Boston, DC, Toronto, Philadelphia... all pretty close by.