I think the idea is that people will drive if their tolerance level for slowness is satisfied. So the amount of traffic will always be high enough to look acceptable for some people, unacceptable for others.
As for parking, in London there are definitely parking lots scattered around the city - can't speak for New York though.
> Like where are they coming from and where are they going?
Probably going between their homes and family / friends / shops / entertainment venues / restaurants.
But in cities these places don't have parking outside. So where are they parking?
Ah I had no idea and would never have guessed that - thanks.
You won't always be able to park right outside your destination, but between street parking and garages there's definitely parking in many places.
My guess is that even if people living there use a car once a year, you end up with a huge number of cars every day.
I can't imagine the logic of thinking 'I need to go into central London to do something today... I know I'll drive'. Not even just from an environmental standpoint - even without that the stress of navigating London and parking and then leaving your car in such a busy place.
A few years ago I arrived in London at Paddington station and was late for meeting on the other side of the city. I'd been told that taking the Tube could take up to 30 minutes (including changes), so I decided to grab a Taxi. I arrived at my meeting 40 minutes later.
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High commuter rail costs - If you have 2+ people in the car, it's likely equal cost at worst to drive if your origin point is beyond the reach of the subway. This is especially true if you wish to go across the metro and therefore get to pay per-person fares on more than one commuter rail system. Going from 15mi West of Manhattan (NJ burbs) to 15mi East of Manhattan (Nassau County), will run you about $50 per person round-trip. It's not hard to see why no one would take commuter rail with their family of 4 for that trip even if they live next to a CR station and their family on the other side does as well, $200 is a lot of money.
Parking - There's tons of (typically underground) garages in NYC and particularly Manhattan. While you may get gouged if you just randomly turn in to the first garage you see and pay the walkup rate, some minor research on rates can easily get you somewhere to park for $20-35 for a full day in Manhattan. 2 seconds on Spothero and I could park right next to Penn Station 9am-9pm today for ~$22, and that's not a rare exception. This was the case before those services as well, it just required more knowledge of where to look for deals.
Scheduling - Off-peak/late-night frequencies are limited and service is often much slower. PATH (a subway with limited reach) to NJ runs 24/7, but late night you're looking at 40min between trains and the trip time often gains 5-10min as well between maintenance and a less direct routing. And if you don't live next to it's limited reach, you're still driving after that. On the actual commuter rail last trip is typically ~1AM and the last few trains of the night have 1-1.5hrs between trains on many lines. I could be back home by car before I even get on the train in Penn Station if I'm particularly unlucky on timing for when the concert I'm seeing ends.
Infrastructure - There's 4 roads to get across the Hudson from NJ in the region, and 2 of them go into Manhattan. Not hard for an accident or minor disruption to make going through Manhattan the only way you're getting across to go to the other side in a sane period of time. The limitations of NYC's "ring" roads also mean you can't necessarily easily just go the longer way around the opposite side of the metro.
There's plenty of areas even within NYC that are poorly served by transit services, to say nothing of the suburbs. When the trip takes 4 transfers to get there, it's a lot less appealing to take and a lot more at risk of issues, even if it should work in theory.
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I am not suggesting cars are the ideal mode of travel, and I'd like to see further investment in broadening both the reach and service levels of transit services, as well as re-examining fare pricing, but with the current systems/infrastructure being what they are.....yes, there are lots of trips where the sensible choice is to drive.