Yes, It's called Queens, specifically Jackson Heights and Kew Gardens, hundreds of pilots and haggered FA's walking down the streets everywhere. Literally. Golf carts are replaced with honking angry beat up taxis and people that may appear to want to stab you though.

Best family areas "in the city" are in certain areas of Brooklyn like Park Slope, Cobble hill, Carroll Gardens, Williamsburg etc or in Manhattan: Upper West side, Upper East side or West village. Of course all those places listed are incredibly expensive though. Astoria has some decent spots too.

I don't know about out in the other further out areas. I have only lived in Manhattan area with no car and using the subway and bus to get to LGA/JFK. I absolutely loved it there being single. Think it would suck with a family though. Would never want my kids growing up in that environment. Rent is just too insane though and housing purchase prices are pretty much out of reach these days. Not really worth it long term if you ever plan to retire or save any money unless your spouse makes 150K plus as well.