Never been to NYC with kids but just want to chime in with some of the previous responses. Subway is the way to travel if you are trying to save some $$. Google Maps and other subway-specific apps make route planning really easy. Cabs and Uber add up fast, and I think 7day subway passes are a thing. We like the passes because they give you a margin for error if you miss a stop or accidentally get on the wrong train—without the pass, you may have to pay again when you re-route. But again, with four people cabs and ubers may be a better value, and you can just buy single subway tickets when the route is direct or convenient.
Also—you are going to take your lumps on food costs. Don’t know how frugal you’re interested in being, but we’ve bought breakfast bars and put juice in the room fridge to at least save on breakfast a couple days. But again, there are some great breakfast/brunch options...Sadelle’s is great, the lox tower is cool and delicious. You’ll need reservations there. Clinton Street Bakery is great too, but the wait can be long. Anyway, I’m rambling.
100% do Top of the Rock. A Night or Day visit each has its own unique appeal.
Met is awesome of course. The Weapons/Armor hall is super cool, as is Egyptian exhibit.
Natural History has some appeal for younger kids, I think, if they’re into dinosaurs.
Block out some time for Central Park, for sure. AND IF YOU DON’T READ ANYTHING ELSE I SAY, READ THIS: Don’t let your kids talk you into a carriage ride. Scam and terrible in every way. Spend the $50 at Dylan’s Candy.
Also—get a life-changing cookie at Levain Bakery. There’s a location near Central Park.
That’s all I got for now. Just wait for Spanky to come along and offer the best advice.