Do you mean New York state or New York city? I'm going to assume you mean NYC since you're talking about "big cities".
Well, I went there on vacation a couple years ago (definitely the best vacation I've been on). We stayed in NJ right by the border and just came over every day.
What it's like depends on what area you're in. In uptown Manhattan, it's just like how you'd imagine it. People everywhere, bright lights, lots of sounds, overall awesome. Then in downtown it's a lot of offices and businesspeople and less touristy. I don't know about the other burrows, but none of them are quite like Manhattan. They're still big city-ish though. There are a million things to see and places to go to.
I'd definitely recommend it. It was so much fun! See the tourist destinations you can, but it's also just as fun to walk the streets, take the subway, etc.