I did practically the same like two weeks ago! Here's some tips:

1. You Want To Get Around: get yourself a MetroCard. DO IT. At any subway station you can get a 7-day Unlimited pass for $32. When you get a 'regular' pass it's $2.50 every time you want to get into the subway - which in my case was often. If you only use it for one roundtrip every day, it's worth it. The other three days I'd suggest doing per-ride and planning around that, or getting another 7-day if you feel like traveling. Also: you can get on the Roosevelt Island cablecar with your MetroCard. Also, the Citymapper app is FANTASTIC when you can get wifi. Do note that the time indication is kinda off.

2. You Want A View: you kinda have to. Stay the hell away from the Empire State building. Not worth the hours of waiting. I found the Rockefeller Center's top floor (dubbed Top of the Rock) to be way better and less touristy.

3. You Want A Museum: the best thing about Top of the Rock is that at the Top of the Rock desk, you can get a combo ticket to the MoMa. Saves you about $15 I think, and the ticket to the MoMa also gives you free access to MoMa PS1 in Brooklyn, so basically an entire day of things to do for $44. I didn't go to the Guggenheim or one of the other famous museums - but there are plenty for you to enjoy.

4. You Want the Food: I found that the area around Fulton Street subway station has lots of food restaurants. There's a TripAdvisor app which saves a lot of restaurants, ATM's and attractions on your device. It's how I found some really neat places I'd otherwise not go to.

5. You Want the Culture: lots of places that are hidden. I recommend the Chelsea Market (great food and awesome place) and the High Line that's next to it (although it's a bit touristy nowadays). Williamsburg is up-and-coming and Brooklyn definitely has character but I didn't get to spend that much time there.

6. You Want to Feel Like A Local: I think nowaypablo can help here.

For me, the best way to enjoy NYC is to just explore and go in with only a loose plan. Stroll around places like DUMBO, the Flatiron district, Upper East Side, Central Park, and you'll go where 90% of tourists don't bother with.