Here's some helpful tips for Manhattan:
Manhattan is generally more expensive than other US cities (aside for SF, DC, and to a certain extent Chicago is comparable) so plan accordingly. Brooklyn is a great alternative if you still want an urban feel but pay a little less (watch out though because it's not THAT much cheaper and places like Williamsburg, where it's very hip and young, are just as expensive.
Subway system is great within Manhattan but to other boroughs and New Jersey (called the PATH) isn't as ubiquitous so you may need to use buses if you're looking to take public transportation. You can always get taxi's or ubers because they are all around so have no fear if you don't like public transportation or are overwhelmed by trying to find directions
USE YELP! Don't go to the tourist traps or chain restaurants, New York has some of the finest cuisine in America and there are even great hole-in-the-wall places and casual dining places that have phenomenal food at a very affordable price. Some quintessential items: fresh bagels (many good places, I prefer Ess-A bagel because its close to me), chicken over rice at the Halal Guys cart, New York style pizza (honestly, most pie places make a decent NY slice so any random place will do), and the reuben at Katz Deli. Obviously there are tons of other places but these are some of the hallmark items of New York. If you're looking to go to a particular spot, MAKE RESERVATIONS. New York social culture revolves around getting drinks and brunch so don't expect to just walk into a good restaurant and get a table within 10 minutes - you WILL have to wait a long time.
Tbh I couldn't recommend many of the big sightseeing places because as a resident they don't particularly interest me but some places I would still go to are Central Park, walk across the iconic Brooklyn Bridge. I wouldn't go to the Statue of Liberty but I wouldn't mind having a drink in an outdoor beer garden at Battery Park Gardens where you can get a view of the Statue of Liberty Also I wouldn't go up to the top floor of 30 Rock (or any other skypscraper you have to pay for) but there are great rooftop bars with phenomenal views of the city (Press Lounge is my favorite).
The Arts: I highly recommend the museums, depending on what exhibits are there. Guggenheim, the Whitney, New Museum, MoMa, the Met are some world class museums and if you're into art I highly recommend. Also, the Broadway shows. Yes they have them in other cities but the production and the cast are top-notch in New York. That being said, the classic shows (a la Mama Mia, Phantom of the Opera, Les Miserable) don't attract the top actors/performers anymore so I would recommend shows such as Wicked, Lion King (classic since I was a kid but it's still AMAZEBALLS to this day), and Book of the Mormon are incredible. Also, lots of comedy clubs where local comedians (and MANY celebrities) try out their material.
If you're planning on lodging in Manhattan, you may want to choose your location based on what activities you plan on doing. For example, if you're planning on doing a lot of shopping then you may want to stay either around Midtown (around 5th ave) or Soho. If you're looking to go barhopping I would avoid Upper Manhattan and stay in lower Manhattan below Midtown.
Google Maps, Yelp, Uber are your best friends.
There are tons of stuff to do for anyone of all interests so if anyone has any particular questions feel free to PM me as well.