One of the things I liked the most was the subway and public transportation system. I didn't have a car at the time and the system was relatively cheap. The system allowed me to get back and forth to my job everyday while also enabling me to head down to Manhattan or other boroughs (I was in Queens) for fun. While it did take time, I had time to spare, but not much money so it worked.
The people. NYC has a very diverse set of people, like in many other large cities. In NYC, you can meet anyone, with a broad range of cultures, but you are in control of your own destiny. In my experience, nobody (most) talked to anyone unless they knew someone ahead of time. It was a funny feeling at first, people would be sitting directly across from each other (6 feet/2 meters) - totally ignoring each others' existence. But! If you were interested in getting to know someone you could, most people were receptive when talked to. Sure, there are a few assholes, but there's always assholes in the group. Included in this are roommates, if you manage to get a good set of roommates while there, that's awesome. If you don't, you can always move. I was lucky in this respect.
NYC has pretty much everything you could want to do, plays, movies, museums, beaches, ice skating, gyms, martial arts, the list goes on except mountain stuff, and even then it's within traveling distance. I enjoy snowboarding so that's one of my main reasons for not wanting to live there. I don't have the time to travel that much anymore, unfortunately.
NYC has a huge mount of opportunity in most industries if you're looking for a job. You just have to reach out and capture it, nobody will hand it to you (usually).
The things I didn't like...
The perception of certain areas. The Bronx, Harlem, some parts of Brooklyn and Queens have bad reputations. Some of it is true but mostly not. There are lot of things in these areas you wouldn't see elsewhere in NYC. I feel you wouldn't get an accurate portrayal of NYC if you didn't go to these areas. The key is to not go out asking for trouble by flashing money around or causing people grief (making people look stupid). Walk confidently and with purpose and you won't usually have an issue. I also wouldn't go wandering around these areas in the dark after drinking either.
Initially, I hated the in-your-face sales approaches that vendors typically use. I got used to it, again, act confidently and don't let them take your money unless you really want what they're selling.
I'm not sure how grocery stores in Norway work but NYC is nothing like I ever knew. It was tough getting to them and even then, it was often public market or corner store food. It is somewhat expensive. Wholesale stores typically have better deals, if you can find one (BJs, Costco, Sam's Club, etc).
After awhile I started missing having a front yard to play with my dogs in. I didn't have much of a yard at the apartments I lived at.
It was a very valuable experience. It helped me grow as a person and helped me learn many different things. If I had to do it over again, I would.
That's it for now; if you have any questions feel free to ask me. Good luck in your travels.