Dawg living in NYC here... agree on most everything here.
Food:
Pizza - Juliana's in DUMBO is the best in the city; it's at the foot of the Brooklyn Bridge and delicious. After eating, walk down to waterfront and you can see awesome views of downtown / Brooklyn Bridge. You can walk back across Brooklyn Bridge or take Subway back to manhattan.
On Manhattan, depends how you want to go... cheap and fast or more sit down.
A few places that haven't been mentioned before for sit down are Motorino in E. Village and Otto in W. Village.
NOTE: agree 100% with the poster who said NYC pizza is cheese or minimal toppings. I grew up in the south, but now nothing appeals to me more than a good slice of cheese with some basil
Burgers - Whitman's in E. village is good, but can be a wait. Have also been to Benson's down south of Houston ("How-ston... don't get me started...) that had delicious, massive burgers.
Italian - Can spread the gamut here, but I like smaller hole in the wall type places.
Patrizia's on 2nd avenue (~26th st) has good stuff and solid pizza, but can be loud.
Mimi's in midtown east is a hidden gem with a piano bar atmosphere
Activities:
Museums - 9/11 museum is somber, but very well done. It's close to One World Trade observatory, and Battery park so you can see the statue of liberty. If you have time and want to get close to the statue of liberty, you can take ferry to staten island for free, or pony up for a tour to go to the actual island. I think at this point, all of the tours to climb to the crown are taken until February.
Just went to the musuem of natural history (or "zoo without the poo" as I call it) with my parents. Interesting, but San Diego Zoo is cooler.
The Met is interesting if you like art and antiquities (recommend the American wing).
The Intrepid Air & Space is interesting with a bunch of military exhibits / old aircraft, including one of the space shuttles (that probably should have gone to Houston, TX rather than NYC, but I digress...)
Entertainment - If you're not offended easily, a comedy show is always enjoyable, although it's generally 18+ (small cover charge and a 2 drink minimum).
There are broadway shows that are funny and not too girly if you're not a theater nerd, although I haven't seen any shows lately so can't recommend any personally... ask at the TKTS booth what's playing and the folks can give you a run down on what each show is.
Sights - Central Park is really neat. I would recommend finding Belvedere Castle, as it is a really neat spot mid-park and has good views. You can work your way south from there and see the Bethesda fountain / Boat house and "the mall" which are the parts you'll recognize from lots of movies/TV shows.
If you're here before 1/6, the Rock Center tree is a must, but it's crowded. Christmas lights on 5th ave are great too.
Times square - see it once, then avoid it.
Transport:
To/From LGA - Might be cheaper to take the Q70 to the subway, but for your sanity, just pony up and take an Uber. If you're staying in Midtown manhattan, an Uber to midtown from LGA is ~$45, well worth the ease to get you into the city.
Around town - Subway is your friend. Generally, "Uptown" is going north, "downtown" is going south. Buy a metrocard, but unless you're here for a full week, probably best to just use "value" rather than "time" option.
Walking - you'll do a lot of it. Remind your wife and daughter as they make shoe choices that comfort far outstrips fashion when walking around a bunch...
You'll have a blast. If I see you around, I'll definitely give you a "Hail State".
