Never lived in SF but it definitely happens in NYC all the time. Not some deep conversation perhaps but people exchange small talk with strangers on the subway, in parks, cafes etc.
The first time I visited NYC, I was in Manhattan for a trade show and I was expecting everybody to be rude or at least curt. Instead, I found people were incredibly friendly and I had an amazing time. My only disappointment was that at 4am most things were shut down. I thought NYC was supposed to be the city that never sleeps.
Traffic lived up to my expectations though. Driving to and from the hotel was a little stressful.
NYC is full of transplants from other places, so quite a few people know how to hang out and chat. If you're obviously not a New Yorker, they might realize that friendly out-of-town norms apply and engage with you.
But being considerate in New York usually looks like staying out of others' way. It might seem like unfriendliness to out-of-towners, but it's a (perhaps counter-intuitive) form of courtesy.
Lived in NYC for nine years; small talk amongst strangers is definitely not the norm unless there is some shared context (subway breakdown, for example)
Traffic lived up to my expectations though. Driving to and from the hotel was a little stressful.