New York is my absolute favourite city in the world and I'm a repeat visitor.
Fly into Newark if possible. The journey from JFK can be awful and it's long journey by public transport. There's a train from Newark Airport that takes you to Penn Station in midtown in about 30 mins. Just he warned the international terminal on the way home is pretty dire!
Taxis are reasonable and the subway is easy to navigate but walking this the best way to see the city.
We try and stay in a different area each time we visit. We liked the Ludlow in the Lower East side and it's an easy walk over the bridge to Williamsburg which is a fun area to mooch around. Also a fan of the Lotte Palace if you'd prefer something more Centre located.
Food wise, there are so many fantastic non- touristy options. We love the secret burger bar at Le Parker Meridien, brunch at the Spotted Pig, Oyster Bar at the Ace Hotel, Eataly, Momafuku noodle bar. The epic queue at Dominique Ansell Bakery is well worth it. also check out Smorgasberg in Brooklyn. There are some great budget options in Chinatown. I've never been to the Gramercy Tavern but heard great things.
Another vote for the Whitney and MOMA. Visit the Public Library, eat pizza in Bryant Park just behind it. Just wandering around Central Park is lovely. You'll stumble across so much random stuff just by walking. Staten Island Ferry is a good alternative to the Statue of Liberty tour. Highline, Meatpacking District. I really liked the United Nations tour (we saw Kofu Annan standing in front of the General Assembly which was pretty mind blowing). Also take the cable car to Roosevelt Island.
It's a really safe city and surprisingly friendly.
In terms of guides, the Wallpaper ones have some good ideas. The Where Chefs Eat app is really good for food suggestions.