It does sound like a family joke doesn't it? but I think it is an old music-hall joke, the profusion of cemeteries in Queens goes back to the C19th. I heard the joke from a friend who grew up in Queens but now lives near a massive cemetery in Brooklyn...
And I'm afraid I'm no help re accommodation stardazzle, as we stay with our friend whenever we go to NY. Brooklyn is full of urban families, has some great parks, and is a wonderful place to stay. I haven't been to Queens, and have no tips about it (and no point asking my mate I don't think, as he hasn't lived in that bit of the city for 30-odd years).
Generally, I found NY an immensely family-friendly city, it actually caters for kids really well IME. Unlike London, say, lots of families live downtown, so there are playgrounds all over the place, it's easy to find inexpensive but decent places to eat out with kids, and there are loads of fantastic child-oriented activities - we went to a wonderful (free) kids' workshop at the Metropolitan Museum, for instance.
We didn't really have a jetlag problem - we arrived 7ish local time, the 4 yr old fell asleep in the taxi and stayed asleep till next morning, and they adjusted pretty quickly. it was worse after we got back, but only bad for a few days.
Have fun! I'm , would love to go again with the kids (am going without them for work soon though, and that will be good too...)