Despite the fact that NYC is only a 40 minute drive or an hour train ride for, I only visit two or three times a year these days. That being said, there are so many options its hard to give you good advise without knowing what you and your family are into. As you probably already know, NYC is an expensive place to visit. Below are a couple of ideas:

'Top of the Rock' (Rockefeller Center) at night is supposed to be fantastic for photos and an overall view of Manhattan, especially on a clear night (see Bryan's post here https://www.the-digital-picture.com/...-the-rock.aspx

The Intrepid has been docked and open for tours for many years. My wife and 23 year old daughter finally visited the ship last summer and we were pleasantly surprised at how much we enjoyed it. We were especially impressed with the submarine tour, as we got a real sense of what life was like for the crew being underwater for long periods of time.

I've eaten many times in Chinatown as a kid, but ever since we've had kids we stopped going (my kids were and still are very picky and wouldn't try anything on the menu). That being said, if your family likes Chinese food and wants as 'real' as you can get on the east coast, I would give it a try. Chinatown is also a cool place to visit as you get a pretty good sense of the culture even if it is only a for a few blocks. Oh, and they offer Gucci and Lois Vuitton pocketbooks for one tenth of the retail price...

We also have visited Little Italy many times. Umbertos has been consistent over the years but is kind of pricey (as are most NYC restaurants). My favorite hot (spicy) shrimp dish is at Vincent's, again pricey (we don't go there too often). Both of these restaurants have likely had 'mob hits' back in the day, but I think those days are long gone. I gather some famous people come in to both places occasionally for the excellent food. In my experience, there was not that much to see in Little Italy, but if you like Italian food, it is worth the trip.

Not sure if your into museums, but our kids absolutely loved the Museum of Natural History when they were about twelve and ten. We expected them to be bored after an hour or so, but instead we had to drag them out after about four hours. There is a lot to see inside, something for everyone. We've also visited the Guggenheim and found it more for the 'artsy' type (a lot of Picasso and abstract art). We also visited the Museum of Modern Art and found it less appealing to kids, but interesting for adults (especially if your into art history - Rembrandt, van Gogh, etc). Across the street from the Natural History museum is a pretty nice area of Central Park.

Of course there's the Freedom tower, the Empire State Building, the Chrysler Building, etc. Our daughter recently visited the Hudson Yards and enjoyed, very cool architecture and unusual design.

With regard to camera gear, my choice would be kit 1. I think you'll find yourself reaching for the widest angle lens most often for landscape shots. NYC is never 'not crowded' (unless your up between 3am and 5am and shooting photos - hint). When your shooting from a sidewalk, there are always people walking in front of you and there are cars, trucks and buses passing in front of you. Instead of trying to get a clear shot of a landmark building, you might find it easier (and more interesting) to include the bright yellow taxicabs in your photo. By the way, you will not be the only person carrying a DSLR, but don't put your camera bag down for a minute while outside (regardless of what area your in).

Finally, if you happen to be into Jazz (even a little bit) there is a place called the Village Vanguard (in Greenwich Village). The Big Band plays on Monday nights and I'd strongly recommend visiting I've been there with my father as a kid, as a young adult with my buddies and as a father with my kids and always leave with a smile on my face. Some of the best jazz musicians in the world (not necessarily the most famous) will be sitting five feet away from your table if you call ahead and request front row seating (get there early). Occasionally one of the big names sits in for an added bonus.

Sorry for all of the rambling, hope I gave you some ideas that may help.