I'm not the grandparent, but I've looked a lot and I don't think there is a single city. New York is the only place you can reasonably live car free without feeling like you're handicapping yourself to make a statement, but it's also very specific type of city that comes with a lot of other baggage (e.g. expensive, overly dense and urban, arguably not where you want to raise kids, etc).
There are plenty of cities where you can live parts of this life, for example when you're young. But when it's time for a family there's basically nowhere in the US you can avoid the house-and-two-cars typical American lifestyle (except New York City with lots of money).