I checked map, it looks like Six Flags in Jackson, New Jersey is closest to NYC - about 70 miles or a 90-minute drive to get there. I am assuming this is the one you would go to. I have never been there, so can't tell you anything specific.
NYC is fabulous, lots of fun, and lots of things to do. Definitely go to a Broadway show. We enjoy the Museum of Modern Art, there are lots of other museums, Central Park you can spend a couple of days walking around, go to Chinatown and Little Italy and eat your way around the city! Seek out the less expensive places that locals go to for lunch, there are some great restaurants that are not fancy and have great values. Just spend some time walking around Times Square at night to take in all the lights!
I do not know what country you are coming from, but agree with other posters, you do realize it will take an entire day to fly from one side of the country to the other. You could maybe stay in NYC one week or so, then go to other side of country. I enjoy Las Vegas but prefer to stay in the city for only a couple of days, and then rent a car and drive to Valley of Fire state park, Hoover Dam, and Grand Canyon for a few days. There are amazing natural areas within an easy driving distance from Las Vegas. And I don't think there is another city anywhere like Las Vegas! Fly in at night and you can see the classic strip lit up, the airport is very close to the strip.