If I lived in NYC, I would not own a car. We did live in Washington DC (the Very District Itself) for nearly 6 years, but we still needed a car, because it was the only way to go shopping for groceries, etc. Still, while living there, I would regularly go to NYC on business by (a) walking 3 blocks to the Metro station, (b) taking the Metro to Union Station, (c), taking Amtrak to NYC, and (d) walking and/or using taxis in NYC. Coming home, I'd reverse the process.
The fundamental issue with public transit is that unless you have a very dense urban setting, you just can't get around all the places you need to in the time frame required. For vast portions of the US, that just doesn't work all that well.